Latest open access articles published in Acadlore Transactions on Applied Mathematics and Statistics at https://www.acadlore.com/journals/ATAMS https://www.acadlore.com/journals/ATAMS Acadlore en Creative Commons Attribution(CC - BY) ATAMS support@acadlore.com https://www.acadlore.com/article/ATAMS/2025_3_2/atams030202 An optimal homotopy asymptotic framework is developed for the numerical-semi-analytical treatment of the time-dependent generalized Korteweg–de Vries (KdV)-modified gKdV-mKdV equation, a prototypical nonlinear dispersive model featuring concurrent quadratic and cubic nonlinearities. The equation arises widely in optics, fluid mechanics, plasma physics and condensed-matter systems, where the accurate resolution of solitary waves and complex wave interactions is essential. The Optimal Homotopy Asymptotic Method (OHAM) is formulated without reliance on an artificial small parameter and is equipped with optimally selected convergence-control parameters, thereby overcoming limitations of classical perturbation techniques. Within this formulation, a rapidly convergent approximate analytical solution is constructed, and error dynamics are quantified against benchmark solutions. Comparative assessments indicate that OHAM attains high accuracy with modest computational effort, delivering pointwise errors and global norms that are competitive with, or superior to, those obtained by Homotopy Perturbation and Homotopy Analysis methods. The procedure is straightforward to implement, preserves the dispersive-nonlinear balance intrinsic to the gKdV–mKdV dynamics, and accommodates important special cases (KdV and mKdV limits) within a unified treatment. The approach is thus shown to provide a reliable and easily computable route to soliton-bearing solutions and other nonlinear waveforms, supporting applications in waveguides, shallow-water channels, ion-acoustic media and lattice excitations. The methodological clarity and demonstrated accuracy suggest that OHAM can serve as a practical front-line tool for nonlinear PDEs with mixed nonlinearities and higher-order dispersion, and that its convergence-control strategy can be extended to related integrable and near-integrable models. 06-29-2025 <![CDATA[ An optimal homotopy asymptotic framework is developed for the numerical-semi-analytical treatment of the time-dependent generalized Korteweg–de Vries (KdV)-modified gKdV-mKdV equation, a prototypical nonlinear dispersive model featuring concurrent quadratic and cubic nonlinearities. The equation arises widely in optics, fluid mechanics, plasma physics and condensed-matter systems, where the accurate resolution of solitary waves and complex wave interactions is essential. The Optimal Homotopy Asymptotic Method (OHAM) is formulated without reliance on an artificial small parameter and is equipped with optimally selected convergence-control parameters, thereby overcoming limitations of classical perturbation techniques. Within this formulation, a rapidly convergent approximate analytical solution is constructed, and error dynamics are quantified against benchmark solutions. Comparative assessments indicate that OHAM attains high accuracy with modest computational effort, delivering pointwise errors and global norms that are competitive with, or superior to, those obtained by Homotopy Perturbation and Homotopy Analysis methods. The procedure is straightforward to implement, preserves the dispersive-nonlinear balance intrinsic to the gKdV–mKdV dynamics, and accommodates important special cases (KdV and mKdV limits) within a unified treatment. The approach is thus shown to provide a reliable and easily computable route to soliton-bearing solutions and other nonlinear waveforms, supporting applications in waveguides, shallow-water channels, ion-acoustic media and lattice excitations. The methodological clarity and demonstrated accuracy suggest that OHAM can serve as a practical front-line tool for nonlinear PDEs with mixed nonlinearities and higher-order dispersion, and that its convergence-control strategy can be extended to related integrable and near-integrable models. ]]> Optimal Homotopy Asymptotic Treatment of the Generalised KdV-mKdV Equation for Nonlinear Dispersive Waves zakir ullah doi: 10.56578/atams030202 Acadlore Transactions on Applied Mathematics and Statistics 06-29-2025 Acadlore Transactions on Applied Mathematics and Statistics 06-29-2025 2025 3 2 Article 101 10.56578/atams030202 https://www.acadlore.com/article/ATAMS/2025_3_2/atams030202 https://www.acadlore.com/article/ATAMS/2025_3_2/atams030201 To investigate the dynamic response and potential structural degradation of carbon fiber sucker rod strings during operation, a torsional vibration model incorporating helical buckling-induced torque excitation has been developed. In this model, the upper suspension boundary condition is idealized as a torsional spring, whose stiffness is determined as a function of both axial displacement and applied load at the suspension point. The torsional stiffness is categorized into time-dependent and mean (average) components, both of which are examined through numerical simulation using the finite difference method. The results reveal pronounced torsional oscillations at the upper section of the rod string, indicating significant torsional deformation of the suspension assembly. A non-monotonic relationship is observed between stroke length and vibration amplitude, wherein torsional vibration initially intensifies with increasing stroke before attenuating, suggesting the presence of resonance phenomena within specific operational ranges. The simulations further demonstrate that time-varying and average torsional stiffnesses yield comparable influences on the overall torsional response. Helical buckling deformation is shown to play a critical role in amplifying torsional stress, with the induced torque predominantly localized in the mid-to-lower segments of the wellbore. The presented model provides an essential theoretical framework for understanding the complex interaction between axial deformation and torsional instability, offering new insights into the mechanisms that may precipitate longitudinal splitting or fatigue failure in carbon fiber sucker rod strings. These findings are expected to support the optimization of rod string design and operational strategies in advanced artificial lift systems. 06-29-2025 <![CDATA[ To investigate the dynamic response and potential structural degradation of carbon fiber sucker rod strings during operation, a torsional vibration model incorporating helical buckling-induced torque excitation has been developed. In this model, the upper suspension boundary condition is idealized as a torsional spring, whose stiffness is determined as a function of both axial displacement and applied load at the suspension point. The torsional stiffness is categorized into time-dependent and mean (average) components, both of which are examined through numerical simulation using the finite difference method. The results reveal pronounced torsional oscillations at the upper section of the rod string, indicating significant torsional deformation of the suspension assembly. A non-monotonic relationship is observed between stroke length and vibration amplitude, wherein torsional vibration initially intensifies with increasing stroke before attenuating, suggesting the presence of resonance phenomena within specific operational ranges. The simulations further demonstrate that time-varying and average torsional stiffnesses yield comparable influences on the overall torsional response. Helical buckling deformation is shown to play a critical role in amplifying torsional stress, with the induced torque predominantly localized in the mid-to-lower segments of the wellbore. The presented model provides an essential theoretical framework for understanding the complex interaction between axial deformation and torsional instability, offering new insights into the mechanisms that may precipitate longitudinal splitting or fatigue failure in carbon fiber sucker rod strings. These findings are expected to support the optimization of rod string design and operational strategies in advanced artificial lift systems. ]]> Simulation and Analysis of Torsional Vibrations in Carbon Fiber Sucker Rod Strings Induced by Helical Buckling Deformation xiurong sun chao yu jialin yang ruiju zhao doi: 10.56578/atams030201 Acadlore Transactions on Applied Mathematics and Statistics 06-29-2025 Acadlore Transactions on Applied Mathematics and Statistics 06-29-2025 2025 3 2 Article 83 10.56578/atams030201 https://www.acadlore.com/article/ATAMS/2025_3_2/atams030201 https://www.acadlore.com/article/ATAMS/2025_3_1/atams030105 This study presents a vibrational analysis of an elastic bar, a fundamental element in continuous systems. The primary objective is to evaluate the vibrational response of a uniform elastic bar under various boundary conditions, including Dirichlet, Neumann, and mixed types. Both numerical and analytical techniques—specifically the finite element method (FEM) and the method of separation of variables—are employed to determine the eigenfrequencies and mode shapes of the bar. The governing equation for a uniform torsional bar, along with its natural boundary conditions, is formulated and solved using separation of variables, leading to coupled equations. Solutions are derived for multiple end conditions, and dispersion (frequency) equations are obtained to compute the eigenvalues. Root-finding methods are used to extract natural frequencies and corresponding eigenfunctions. The vibrational response is visualized for different cases and compared with existing results in the literature. Findings reveal that the natural frequencies of torsional bars are affected by additional elements such as attached masses, springs, and dampers. This investigation enhances the understanding of elastic bar dynamics and provides useful insights for the design and optimization of structural systems involving torsional bars. 03-30-2025 <![CDATA[ This study presents a vibrational analysis of an elastic bar, a fundamental element in continuous systems. The primary objective is to evaluate the vibrational response of a uniform elastic bar under various boundary conditions, including Dirichlet, Neumann, and mixed types. Both numerical and analytical techniques—specifically the finite element method (FEM) and the method of separation of variables—are employed to determine the eigenfrequencies and mode shapes of the bar. The governing equation for a uniform torsional bar, along with its natural boundary conditions, is formulated and solved using separation of variables, leading to coupled equations. Solutions are derived for multiple end conditions, and dispersion (frequency) equations are obtained to compute the eigenvalues. Root-finding methods are used to extract natural frequencies and corresponding eigenfunctions. The vibrational response is visualized for different cases and compared with existing results in the literature. Findings reveal that the natural frequencies of torsional bars are affected by additional elements such as attached masses, springs, and dampers. This investigation enhances the understanding of elastic bar dynamics and provides useful insights for the design and optimization of structural systems involving torsional bars. ]]> Vibrational Response of a Continuous System: Analysis of Elastic Bar Behavior under Multiple Boundary Conditions umara bushra talha anwar asifa doi: 10.56578/atams030105 Acadlore Transactions on Applied Mathematics and Statistics 03-30-2025 Acadlore Transactions on Applied Mathematics and Statistics 03-30-2025 2025 3 1 Article 65 10.56578/atams030105 https://www.acadlore.com/article/ATAMS/2025_3_1/atams030105 https://www.acadlore.com/article/ATAMS/2025_3_1/atams030104 Automobiles play a vital role in daily life, providing suitable and efficient transportation for work, school, and errands. They also support essential services like emergency response, goods delivery, and public transportation systems. This increased variety means that car manufacturers are competing intensely to attract customers and maximize their profits. However, making the right choice when buying a car can be challenging due to the wide range of factors to consider. This study introduces a new approach that uses Dombi operators combined with T-spherical fuzzy numbers (T-SFNs) to help improve the decision-making process. This method reduces the uncertainty and imprecision that often comes with decision-making, especially when selecting a car. The aim is to help customers make better, more informed choices and avoid financial difficulties. To achieve this, the study develops several innovative operators namely T-spherical fuzzy Dombi weighted averaging (T-SFDWA), T-spherical fuzzy Dombi ordered weighted averaging (T-SFDOWA), T-spherical fuzzy Dombi weighted geometric (T-SFDWG), T-spherical fuzzy Dombi ordered weighted geometric (T-SFDOWG). These methods offer flexibility, suppleness and can adapt to real-world problems where factors are constantly changing. By managing uncertainty and hesitation effectively, these approaches help decision-makers evaluate complex situations with multiple variables. A practical example, such as choosing a car, demonstrates how these approaches can evaluate important criteria like price, safety, and fuel efficiency. Ultimately, these methods ensure that consumers can make the best decision, even in uncertain and complex situations. 03-30-2025 <![CDATA[ <p>Automobiles play a vital role in daily life, providing suitable and efficient transportation for work, school, and errands. They also support essential services like emergency response, goods delivery, and public transportation systems. This increased variety means that car manufacturers are competing intensely to attract customers and maximize their profits. However, making the right choice when buying a car can be challenging due to the wide range of factors to consider. This study introduces a new approach that uses Dombi operators combined with T-spherical fuzzy numbers (T-SFNs) to help improve the decision-making process. This method reduces the uncertainty and imprecision that often comes with decision-making, especially when selecting a car. The aim is to help customers make better, more informed choices and avoid financial difficulties. To achieve this, the study develops several innovative operators namely T-spherical fuzzy Dombi weighted averaging (T-SFDWA), T-spherical fuzzy Dombi ordered weighted averaging (T-SFDOWA), T-spherical fuzzy Dombi weighted geometric (T-SFDWG), T-spherical fuzzy Dombi ordered weighted geometric (T-SFDOWG). These methods offer flexibility, suppleness and can adapt to real-world problems where factors are constantly changing. By managing uncertainty and hesitation effectively, these approaches help decision-makers evaluate complex situations with multiple variables. A practical example, such as choosing a car, demonstrates how these approaches can evaluate important criteria like price, safety, and fuel efficiency. Ultimately, these methods ensure that consumers can make the best decision, even in uncertain and complex situations.</p> ]]> Mathematical Model to Evaluate of Client Behavior in the Automobile Sector Based on T-Spherical Fuzzy Information within Dombi Environment muhammad altaf khan khaista rahman doi: 10.56578/atams030104 Acadlore Transactions on Applied Mathematics and Statistics 03-30-2025 Acadlore Transactions on Applied Mathematics and Statistics 03-30-2025 2025 3 1 Article 52 10.56578/atams030104 https://www.acadlore.com/article/ATAMS/2025_3_1/atams030104 https://www.acadlore.com/article/ATAMS/2025_3_1/atams030103 Neutrosophy is a special area of philosophy that explains the nature, genesis and scope of neutralities, like the interactions with diverse ideational hues. It showed the degree of indeterminacy as an independent component that was the extension of an intuitionistic set. In this paper, the interpretation of the linear equation of type $\mathcal{A}\mathcal{X} +\mathcal{B} =\mathcal{C}$ are discussed in a neutrosophic environment. It is observed that the equations $\mathcal{A}\mathcal{X} +\mathcal{B} =\mathcal{C}$, $\mathcal{A}\mathcal{X} =\mathcal{C} -\mathcal{B}$ and $\mathcal{A}\mathcal{X} -\mathcal{C} =-\mathcal{B}$ are same and their solution are also same in crisp sense. But, in the neutrosophic sense, the solutions to the above equations are different. Mathematical operations on intervals are considered for the purpose of solution and analysis. Further, an application of budgeting-financing is described with the help of neutrosophic fuzzy equation. 03-30-2025 <![CDATA[ <p>Neutrosophy is a special area of philosophy that explains the nature, genesis and scope of neutralities, like the interactions with diverse ideational hues. It showed the degree of indeterminacy as an independent component that was the extension of an intuitionistic set. In this paper, the interpretation of the linear equation of type $\mathcal{A}\mathcal{X} +\mathcal{B} =\mathcal{C}$ are discussed in a neutrosophic environment. It is observed that the equations $\mathcal{A}\mathcal{X} +\mathcal{B} =\mathcal{C}$, $\mathcal{A}\mathcal{X} =\mathcal{C} -\mathcal{B}$ and $\mathcal{A}\mathcal{X} -\mathcal{C} =-\mathcal{B}$ are same and their solution are also same in crisp sense. But, in the neutrosophic sense, the solutions to the above equations are different. Mathematical operations on intervals are considered for the purpose of solution and analysis. Further, an application of budgeting-financing is described with the help of neutrosophic fuzzy equation.</p> ]]> Solution and Interpretation of Neutrosophic Fuzzy Equation with Applications aditi biswas kamal hossain gazi payal singh sankar prasad mondal doi: 10.56578/atams030103 Acadlore Transactions on Applied Mathematics and Statistics 03-30-2025 Acadlore Transactions on Applied Mathematics and Statistics 03-30-2025 2025 3 1 Article 24 10.56578/atams030103 https://www.acadlore.com/article/ATAMS/2025_3_1/atams030103 https://www.acadlore.com/article/ATAMS/2025_3_1/atams030102 Accurate and robust image segmentation remains a fundamental challenge in computer vision, particularly in the presence of intensity inhomogeneity, noise, and weak object boundaries. To address these challenges, we propose a Robust Pythagorean Fuzzy Energy-Based Level Set (RPFELS) model, which integrates a novel fuzzy energy formulation with level set evolution to enhance segmentation precision and resilience against noise. The model introduces a Pythagorean fuzzy divergence term to refine energy optimization, ensuring adaptive boundary preservation and reducing sensitivity to intensity variations. Additionally, a bounded fuzzy energy constraint is incorporated to ensure numerical stability and prevent energy leakage during evolution. Extensive experiments on benchmark datasets, including medical and natural images, validate the effectiveness of RPFELS. The model consistently outperforms recent selective segmentation methods in terms of Dice Score, Jaccard Index, and Hausdorff Distance, achieving superior segmentation accuracy and reduced boundary errors. Furthermore, a detailed statistical significance analysis using paired t-tests confirms that the observed improvements are statistically significant (p-value $ 03-30-2025 <![CDATA[ <p>Accurate and robust image segmentation remains a fundamental challenge in computer vision, particularly in the presence of intensity inhomogeneity, noise, and weak object boundaries. To address these challenges, we propose a Robust Pythagorean Fuzzy Energy-Based Level Set (RPFELS) model, which integrates a novel fuzzy energy formulation with level set evolution to enhance segmentation precision and resilience against noise. The model introduces a Pythagorean fuzzy divergence term to refine energy optimization, ensuring adaptive boundary preservation and reducing sensitivity to intensity variations. Additionally, a bounded fuzzy energy constraint is incorporated to ensure numerical stability and prevent energy leakage during evolution. Extensive experiments on benchmark datasets, including medical and natural images, validate the effectiveness of RPFELS. The model consistently outperforms recent selective segmentation methods in terms of Dice Score, Jaccard Index, and Hausdorff Distance, achieving superior segmentation accuracy and reduced boundary errors. Furthermore, a detailed statistical significance analysis using paired t-tests confirms that the observed improvements are statistically significant (p-value $<$ 0.01), reinforcing the reliability of the proposed approach. Moreover, RPFELS exhibits higher computational efficiency, achieving faster convergence rates compared to existing methods. These findings highlight the robustness and versatility of the proposed approach in handling challenging segmentation scenarios, making it suitable for applications in medical imaging, remote sensing, and industrial defect detection. By ensuring bounded energy evolution and statistically validated performance gains, our model sets a new benchmark in selective segmentation.</p> ]]> An Uncertainty-Driven Fuzzy Energy Level Set Model for Robust and Adaptive Image Segmentation muhammad zeeshan naeem doi: 10.56578/atams030102 Acadlore Transactions on Applied Mathematics and Statistics 03-30-2025 Acadlore Transactions on Applied Mathematics and Statistics 03-30-2025 2025 3 1 Article 13 10.56578/atams030102 https://www.acadlore.com/article/ATAMS/2025_3_1/atams030102 https://www.acadlore.com/article/ATAMS/2025_3_1/atams030101 In order to approximate several roots of nonlinear equations, we presented a novel family of two-step optimal iterative methods in this study. The method is fourth-order convergent, requiring just four function evaluations each iteration, and it is optimal in terms of Kung-Traub's conjecture. We use complex dynamical analysis, often known as basins of attraction, to study local convergence and dynamical behavior. Numerical experiments on nonlinear problems in biomedical engineering are carried out to determine the method's efficiency and robustness in comparison to other methods. In terms of convergence rate, computational complexity, and stability, numerical findings show that the novel approach outperforms the well-known existing algorithms, especially for functions with higher multiplicities of order. 03-30-2025 <![CDATA[ <p>In order to approximate several roots of nonlinear equations, we presented a novel family of two-step optimal iterative methods in this study. The method is fourth-order convergent, requiring just four function evaluations each iteration, and it is optimal in terms of Kung-Traub's conjecture. We use complex dynamical analysis, often known as basins of attraction, to study local convergence and dynamical behavior. Numerical experiments on nonlinear problems in biomedical engineering are carried out to determine the method's efficiency and robustness in comparison to other methods. In terms of convergence rate, computational complexity, and stability, numerical findings show that the novel approach outperforms the well-known existing algorithms, especially for functions with higher multiplicities of order.</p> ]]> Optimized Computational Schemes for Finding Multiple Roots in Nonlinear Biomedical Engineering Problems mudassir shams nasreen kausar doi: 10.56578/atams030101 Acadlore Transactions on Applied Mathematics and Statistics 03-30-2025 Acadlore Transactions on Applied Mathematics and Statistics 03-30-2025 2025 3 1 Article 1 10.56578/atams030101 https://www.acadlore.com/article/ATAMS/2025_3_1/atams030101 https://www.acadlore.com/article/ATAMS/2024_2_4/atams020405 In this paper, we derive a new conjugate gradient (CG) direction with random parameters which are obtained by minimizing the deviation between search direction matrix and self-scaled memoryless Broyden-Fletcher-Goldfard-Shanno (BFGS) update. We propose a new spectral three-term CG algorithm and establish the global convergence of new method for uniformly convex functions and general nonlinear functions, respectively. Numerical experiments show that our method has nice numerical performance on nonconvex functions and supply chain problems. 12-30-2024 <![CDATA[ <p>In this paper, we derive a new conjugate gradient (CG) direction with random parameters which are obtained by minimizing the deviation between search direction matrix and self-scaled memoryless Broyden-Fletcher-Goldfard-Shanno (BFGS) update. We propose a new spectral three-term CG algorithm and establish the global convergence of new method for uniformly convex functions and general nonlinear functions, respectively. Numerical experiments show that our method has nice numerical performance on nonconvex functions and supply chain problems.</p> ]]> A New Spectral Three-Term Conjugate Gradient Method for Unconstrained Optimization and Its Application mingyuan cao siqi liu ruobing mei zongxu li yueting yang doi: 10.56578/atams020405 Acadlore Transactions on Applied Mathematics and Statistics 12-30-2024 Acadlore Transactions on Applied Mathematics and Statistics 12-30-2024 2024 2 4 Article 252 10.56578/atams020405 https://www.acadlore.com/article/ATAMS/2024_2_4/atams020405 https://www.acadlore.com/article/ATAMS/2024_2_4/atams020404 The forecasting of wheat commodity prices plays a crucial role in mitigating financial risks for stakeholders across the agricultural supply chain. In this study, the predictive performance of three models—Simple Moving Average (SMA), Extreme Gradient Boosting (XGBoost), and a hybrid SMA-XGBoost model—was evaluated to determine their efficacy in capturing both linear trends and complex nonlinear patterns inherent in wheat price data. A 10-lag structure was employed to integrate historical dependencies and seasonal fluctuations, thereby enhancing the accuracy of trend identification. The dataset was partitioned into training (75%) and testing (25%) subsets to facilitate an objective performance assessment. The XGBoost model, known for its capability in modelling nonlinear dependencies, demonstrated the highest forecasting precision, achieving a Mean Absolute Percentage Error (MAPE) of 1.64%. The hybrid SMA-XGBoost model, which leveraged the complementary strengths of both SMA and XGBoost, yielded a MAPE of 1.75%, outperforming the standalone SMA model, which exhibited a MAPE of 2.60%. While the hybrid model displayed slightly lower accuracy than XGBoost, it offered greater stability and robustness by effectively balancing trend extraction and nonlinear adaptability. These findings highlight the hybrid approach as a viable alternative to purely machine learning-based forecasting methods, particularly in scenarios requiring resilience to diverse market fluctuations. The proposed methodology provides a valuable tool for policymakers, agricultural producers, and market analysts seeking to enhance decision-making strategies and optimize risk management within the agricultural sector. 12-30-2024 <![CDATA[ <p>The forecasting of wheat commodity prices plays a crucial role in mitigating financial risks for stakeholders across the agricultural supply chain. In this study, the predictive performance of three models—Simple Moving Average (SMA), Extreme Gradient Boosting (XGBoost), and a hybrid SMA-XGBoost model—was evaluated to determine their efficacy in capturing both linear trends and complex nonlinear patterns inherent in wheat price data. A 10-lag structure was employed to integrate historical dependencies and seasonal fluctuations, thereby enhancing the accuracy of trend identification. The dataset was partitioned into training (75%) and testing (25%) subsets to facilitate an objective performance assessment. The XGBoost model, known for its capability in modelling nonlinear dependencies, demonstrated the highest forecasting precision, achieving a Mean Absolute Percentage Error (MAPE) of 1.64%. The hybrid SMA-XGBoost model, which leveraged the complementary strengths of both SMA and XGBoost, yielded a MAPE of 1.75%, outperforming the standalone SMA model, which exhibited a MAPE of 2.60%. While the hybrid model displayed slightly lower accuracy than XGBoost, it offered greater stability and robustness by effectively balancing trend extraction and nonlinear adaptability. These findings highlight the hybrid approach as a viable alternative to purely machine learning-based forecasting methods, particularly in scenarios requiring resilience to diverse market fluctuations. The proposed methodology provides a valuable tool for policymakers, agricultural producers, and market analysts seeking to enhance decision-making strategies and optimize risk management within the agricultural sector.</p> ]]> A Hybrid Simple Moving Average and XGBoost Approach for Enhanced Wheat Commodity Price Forecasting muhammad sahid muhamad ramdhani gumgum darmawan doi: 10.56578/atams020404 Acadlore Transactions on Applied Mathematics and Statistics 12-30-2024 Acadlore Transactions on Applied Mathematics and Statistics 12-30-2024 2024 2 4 Article 238 10.56578/atams020404 https://www.acadlore.com/article/ATAMS/2024_2_4/atams020404 https://www.acadlore.com/article/ATAMS/2024_2_4/atams020403 As a rapidly developing nation, India faces an urgent need to diversify its energy portfolio to ensure long-term sustainability and energy security. Biomass energy, as a renewable and sustainable resource, has the potential to play a crucial role in achieving these objectives. Its integration into the national energy framework, however, is hindered by multiple challenges, including technological limitations, socio-economic constraints, and environmental concerns. Despite its advantages—such as reducing greenhouse gas emissions, promoting economic growth, managing waste, and preserving biodiversity—several barriers must be systematically analyzed to facilitate its widespread adoption. In this study, a structured approach is employed to identify and evaluate the key challenges associated with biomass energy adaptation in India. The Decision-Making Trial and Evaluation Laboratory (DEMATEL) methodology is applied to determine the relative importance of these challenges, offering insights into the most critical criteria that require focused intervention. The findings of this study are expected to provide a strategic foundation for policymakers and stakeholders in formulating effective policies and technological solutions to enhance the viability of biomass energy in India's energy transition. 12-30-2024 <![CDATA[ As a rapidly developing nation, India faces an urgent need to diversify its energy portfolio to ensure long-term sustainability and energy security. Biomass energy, as a renewable and sustainable resource, has the potential to play a crucial role in achieving these objectives. Its integration into the national energy framework, however, is hindered by multiple challenges, including technological limitations, socio-economic constraints, and environmental concerns. Despite its advantages—such as reducing greenhouse gas emissions, promoting economic growth, managing waste, and preserving biodiversity—several barriers must be systematically analyzed to facilitate its widespread adoption. In this study, a structured approach is employed to identify and evaluate the key challenges associated with biomass energy adaptation in India. The Decision-Making Trial and Evaluation Laboratory (DEMATEL) methodology is applied to determine the relative importance of these challenges, offering insights into the most critical criteria that require focused intervention. The findings of this study are expected to provide a strategic foundation for policymakers and stakeholders in formulating effective policies and technological solutions to enhance the viability of biomass energy in India's energy transition. ]]> Challenges in the Adaptation of Biomass Energy in India: A Multi-Criteria Decision-Making Approach Using DEMATEL tripti basuri srabani guria das aditi biswas kamal hossain gazi sankar prasad mondal arijit ghosh doi: 10.56578/atams020403 Acadlore Transactions on Applied Mathematics and Statistics 12-30-2024 Acadlore Transactions on Applied Mathematics and Statistics 12-30-2024 2024 2 4 Article 222 10.56578/atams020403 https://www.acadlore.com/article/ATAMS/2024_2_4/atams020403 https://www.acadlore.com/article/ATAMS/2024_2_4/atams020402 Graph structures (GSs) have appeared as a robust mathematical framework for modelling and resolving complex combinatorial problems across diverse realms. At the same time, the linear Diophantine fuzzy set (LDFS) is a noteworthy expansion of the conventional concepts of the fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PFS), and q-Rung orthopair fuzzy set (q-ROFS). The LDFS framework introduces a flexible parameterization strategy that independently relaxes membership and non-membership restraints through reference parameters, thereby attaining enhanced expressiveness in apprehending ambiguous real-world phenomena. In this paper, a novel concept of linear Diophantine fuzzy graph structure (LDFGS) is introduced as a generalization of intuitionistic fuzzy graph structure (IFGS) and linear Diophantine fuzzy graph (LDFG) to GSs. Several cardinal fundamental notions in LDFGSs, including $\breve{\rho}_i$-edge, $\breve{\rho}_i$-path, strength of $\breve{\rho}_i$-path, $\breve{\rho}_i$-strength of connectedness, $\breve{\rho}_i$-degree of a vertex, degree of a vertex, total $\breve{\rho}_i$-degree of a vertex, and the total degree of a vertex in an LDFGS are discussed. Additionally, $\breve{\rho}_i$-size of an LDFGS, the size of an LDFGS, and the order of an LDFGS are studied. Meanwhile, the ideas of the maximal product of two LDFGSs, strong LDFGS, degree, and $\breve{\rho}_i$-degree of the maximal product are introduced with several concrete illustrations. To empirically validate the efficacy and practical utility of the proposed LDFGS framework, this study presents a case study analyzing road crime patterns across heterogeneous urban regions in Sindh province, Pakistan. 12-30-2024 <![CDATA[ <p>Graph structures (GSs) have appeared as a robust mathematical framework for modelling and resolving complex combinatorial problems across diverse realms. At the same time, the linear Diophantine fuzzy set (LDFS) is a noteworthy expansion of the conventional concepts of the fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PFS), and q-Rung orthopair fuzzy set (q-ROFS). The LDFS framework introduces a flexible parameterization strategy that independently relaxes membership and non-membership restraints through reference parameters, thereby attaining enhanced expressiveness in apprehending ambiguous real-world phenomena. In this paper, a novel concept of linear Diophantine fuzzy graph structure (LDFGS) is introduced as a generalization of intuitionistic fuzzy graph structure (IFGS) and linear Diophantine fuzzy graph (LDFG) to GSs. Several cardinal fundamental notions in LDFGSs, including $\breve{\rho}_i$-edge, $\breve{\rho}_i$-path, strength of $\breve{\rho}_i$-path, $\breve{\rho}_i$-strength of connectedness, $\breve{\rho}_i$-degree of a vertex, degree of a vertex, total $\breve{\rho}_i$-degree of a vertex, and the total degree of a vertex in an LDFGS are discussed. Additionally, $\breve{\rho}_i$-size of an LDFGS, the size of an LDFGS, and the order of an LDFGS are studied. Meanwhile, the ideas of the maximal product of two LDFGSs, strong LDFGS, degree, and $\breve{\rho}_i$-degree of the maximal product are introduced with several concrete illustrations. To empirically validate the efficacy and practical utility of the proposed LDFGS framework, this study presents a case study analyzing road crime patterns across heterogeneous urban regions in Sindh province, Pakistan.</p> ]]> Linear Diophantine Fuzzy Graph Structures: Theoretical Foundations and Applications in Road Crime Detection rizwan gul doi: 10.56578/atams020402 Acadlore Transactions on Applied Mathematics and Statistics 12-30-2024 Acadlore Transactions on Applied Mathematics and Statistics 12-30-2024 2024 2 4 Article 193 10.56578/atams020402 https://www.acadlore.com/article/ATAMS/2024_2_4/atams020402 https://www.acadlore.com/article/ATAMS/2024_2_4/atams020401 Nanofluids, which are suspensions of nanoparticles in base fluids, have demonstrated considerable potential in enhancing thermal conductivity, energy storage, and lubrication properties, as well as improving the cooling efficiency of electronic devices. Despite their promising applications, the industrial utilization of nanofluids remains in the early stages, with further research needed to fully explore their capabilities. This study investigates a generalized nanofluid model, incorporating fractal-fractional derivative (FFD), to better understand the thermophysical behaviors in vertical channel flow. The nanofluid consists of polystyrene nanoparticles uniformly dispersed in kerosene oil. An exact solution to the model is obtained by employing the Laplace transform technique (LTT) in combination with the numerical Zakian’s algorithm. The FFD operator with an exponential kernel is applied to extend the classical nanofluid model. Discretization of the generalized model is achieved using the Crank-Nicolson method, and numerical simulations are performed to solve the resulting equations. The study reveals that, at a nanoparticle volume fraction of 4% (0.04), the heat transfer rate of the nanofluid is significantly higher than that of the base fluid. Furthermore, the enhanced heat transfer leads to improvements in various thermophysical properties, such as viscosity, thermal expansion, and heat capacity, which are crucial for industrial applications. The numerical results are presented graphically to highlight the dependence of the flow and thermal dispersion characteristics on key physical factors. These findings suggest that the use of fractal-fractional models can provide a more accurate representation of nanofluid behavior, particularly for high-precision applications in heat transfer and energy systems. 12-30-2024 <![CDATA[ <p>Nanofluids, which are suspensions of nanoparticles in base fluids, have demonstrated considerable potential in enhancing thermal conductivity, energy storage, and lubrication properties, as well as improving the cooling efficiency of electronic devices. Despite their promising applications, the industrial utilization of nanofluids remains in the early stages, with further research needed to fully explore their capabilities. This study investigates a generalized nanofluid model, incorporating fractal-fractional derivative (FFD), to better understand the thermophysical behaviors in vertical channel flow. The nanofluid consists of polystyrene nanoparticles uniformly dispersed in kerosene oil. An exact solution to the model is obtained by employing the Laplace transform technique (LTT) in combination with the numerical Zakian’s algorithm. The FFD operator with an exponential kernel is applied to extend the classical nanofluid model. Discretization of the generalized model is achieved using the Crank-Nicolson method, and numerical simulations are performed to solve the resulting equations. The study reveals that, at a nanoparticle volume fraction of 4% (0.04), the heat transfer rate of the nanofluid is significantly higher than that of the base fluid. Furthermore, the enhanced heat transfer leads to improvements in various thermophysical properties, such as viscosity, thermal expansion, and heat capacity, which are crucial for industrial applications. The numerical results are presented graphically to highlight the dependence of the flow and thermal dispersion characteristics on key physical factors. These findings suggest that the use of fractal-fractional models can provide a more accurate representation of nanofluid behavior, particularly for high-precision applications in heat transfer and energy systems.</p> ]]> Mathematical Analysis of the Fractal-Fractional Nanofluid Model for Heat Transfer Enhancement in Polystyrene/Kerosene Oil Systems saqib murtaza razi khan zubair ahmad doi: 10.56578/atams020401 Acadlore Transactions on Applied Mathematics and Statistics 12-30-2024 Acadlore Transactions on Applied Mathematics and Statistics 12-30-2024 2024 2 4 Article 180 10.56578/atams020401 https://www.acadlore.com/article/ATAMS/2024_2_4/atams020401 https://www.acadlore.com/article/ATAMS/2024_2_3/atams020305 Efficient classification of interval data presents considerable challenges, particularly when group overlaps and data uncertainty are prevalent. This study introduces an innovative two-stage Mixed Integer Programming (MIP) framework for discriminant analysis (DA), which is designed to minimize misclassification of vertices while effectively addressing the problem of overlapping groups. By incorporating interval data structures, the proposed model captures both the shared characteristics within groups and the distinct separations between them. The first stage of the model focuses on the identification of group-specific boundaries, while the second stage refines classification by incorporating probabilistic estimates of group memberships. A Monte Carlo simulation is employed to evaluate the robustness of the model under conditions of imprecision and noise, and the results demonstrate its superior capability in handling overlapping data and classifying uncertain observations. Validation through numerical experiments illustrates the model’s effectiveness in accurately resolving group overlaps, thereby improving classification performance. The approach offers significant advantages over traditional methods by probabilistically estimating group memberships, thus enhancing decision-making processes in uncertain environments. These findings suggest that the proposed MIP framework holds substantial promise for applications across a range of complex decision-making scenarios, such as those encountered in finance, healthcare, and engineering, where data imprecision is a critical concern. 09-29-2024 <![CDATA[ Efficient classification of interval data presents considerable challenges, particularly when group overlaps and data uncertainty are prevalent. This study introduces an innovative two-stage Mixed Integer Programming (MIP) framework for discriminant analysis (DA), which is designed to minimize misclassification of vertices while effectively addressing the problem of overlapping groups. By incorporating interval data structures, the proposed model captures both the shared characteristics within groups and the distinct separations between them. The first stage of the model focuses on the identification of group-specific boundaries, while the second stage refines classification by incorporating probabilistic estimates of group memberships. A Monte Carlo simulation is employed to evaluate the robustness of the model under conditions of imprecision and noise, and the results demonstrate its superior capability in handling overlapping data and classifying uncertain observations. Validation through numerical experiments illustrates the model’s effectiveness in accurately resolving group overlaps, thereby improving classification performance. The approach offers significant advantages over traditional methods by probabilistically estimating group memberships, thus enhancing decision-making processes in uncertain environments. These findings suggest that the proposed MIP framework holds substantial promise for applications across a range of complex decision-making scenarios, such as those encountered in finance, healthcare, and engineering, where data imprecision is a critical concern. ]]> Optimizing Interval Data Classification Through Two-Stage Mixed Integer Programming: A Discriminant Analysis Perspective sanaz hami hassan kiyadeh javad pourqasem appasamy saraswathi doi: 10.56578/atams020305 Acadlore Transactions on Applied Mathematics and Statistics 09-29-2024 Acadlore Transactions on Applied Mathematics and Statistics 09-29-2024 2024 2 3 Article 169 10.56578/atams020305 https://www.acadlore.com/article/ATAMS/2024_2_3/atams020305 https://www.acadlore.com/article/ATAMS/2024_2_3/atams020304 This study proposes an advanced framework for performance evaluation by extending the Malmquist Productivity Index (MPI) to accommodate interval data, addressing the inherent uncertainty and imprecision frequently encountered in institutional assessments. In many contexts, input-output data are often reported as intervals rather than precise values, which poses significant challenges for evaluating productivity changes. The extended MPI model allows for a more comprehensive analysis of performance by incorporating such interval data, thus providing a robust mechanism for assessing both progress and regression in the productivity of Decision-Making Units (DMUs). A case study on university departments is employed to demonstrate the practical application of this interval-based model. The results highlight notable variations in efficiency and technological advancement, offering valuable insights for institutional decision-makers. The proposed methodology enhances the accuracy of performance evaluation in dynamic and uncertain environments, making it a powerful tool for strategic planning and policy formulation. Furthermore, it is suggested that this interval-based approach offers a significant improvement over traditional models by accounting for the uncertainty present in real-world data. The study contributes to the broader field of strategic performance analytics by advancing the methodological understanding of productivity analysis, offering a more nuanced and reliable framework for institutional assessment. 09-29-2024 <![CDATA[ This study proposes an advanced framework for performance evaluation by extending the Malmquist Productivity Index (MPI) to accommodate interval data, addressing the inherent uncertainty and imprecision frequently encountered in institutional assessments. In many contexts, input-output data are often reported as intervals rather than precise values, which poses significant challenges for evaluating productivity changes. The extended MPI model allows for a more comprehensive analysis of performance by incorporating such interval data, thus providing a robust mechanism for assessing both progress and regression in the productivity of Decision-Making Units (DMUs). A case study on university departments is employed to demonstrate the practical application of this interval-based model. The results highlight notable variations in efficiency and technological advancement, offering valuable insights for institutional decision-makers. The proposed methodology enhances the accuracy of performance evaluation in dynamic and uncertain environments, making it a powerful tool for strategic planning and policy formulation. Furthermore, it is suggested that this interval-based approach offers a significant improvement over traditional models by accounting for the uncertainty present in real-world data. The study contributes to the broader field of strategic performance analytics by advancing the methodological understanding of productivity analysis, offering a more nuanced and reliable framework for institutional assessment. ]]> Strategic Performance Evaluation Using the Interval Malmquist Index for Institutional Assessment bardia khalilian soheil fakheri mohammad fallah doi: 10.56578/atams020304 Acadlore Transactions on Applied Mathematics and Statistics 09-29-2024 Acadlore Transactions on Applied Mathematics and Statistics 09-29-2024 2024 2 3 Article 160 10.56578/atams020304 https://www.acadlore.com/article/ATAMS/2024_2_3/atams020304 https://www.acadlore.com/article/ATAMS/2024_2_3/atams020303 This study investigates the regional logistics efficiency of Sichuan Province, China, from 2011 to 2019, using a combination of the Data Envelopment Analysis-Banker, Charnes, and Cooper (DEA-BCC) model and the Tobit model. The primary objective is to assess the efficiency of the logistics industry and identify the key determinants influencing this efficiency within the context of high-quality development. A comprehensive input-output index system and a set of influencing factor variables were constructed to evaluate logistics performance across various regions of the province. The findings indicate that factors such as the level of economic development, urbanization, and geographical location significantly enhance regional logistics efficiency. In contrast, the level of informatization and the industrial structure exhibit clear inhibitory effects. Specifically, a higher degree of informatization does not necessarily correspond with improved logistics efficiency, potentially due to inefficiencies in technology adoption or uneven infrastructure development. Furthermore, the current industrial structure, with its reliance on traditional industries, may hinder the optimization of logistics systems. Based on these results, several policy recommendations are put forward, including the optimization of the industrial structure, better integration of information technologies in logistics processes, and the strategic utilization of Sichuan’s geographical advantages. This research provides valuable insights for policymakers aiming to enhance logistics efficiency as part of the region’s broader economic development strategy. 09-29-2024 <![CDATA[ This study investigates the regional logistics efficiency of Sichuan Province, China, from 2011 to 2019, using a combination of the Data Envelopment Analysis-Banker, Charnes, and Cooper (DEA-BCC) model and the Tobit model. The primary objective is to assess the efficiency of the logistics industry and identify the key determinants influencing this efficiency within the context of high-quality development. A comprehensive input-output index system and a set of influencing factor variables were constructed to evaluate logistics performance across various regions of the province. The findings indicate that factors such as the level of economic development, urbanization, and geographical location significantly enhance regional logistics efficiency. In contrast, the level of informatization and the industrial structure exhibit clear inhibitory effects. Specifically, a higher degree of informatization does not necessarily correspond with improved logistics efficiency, potentially due to inefficiencies in technology adoption or uneven infrastructure development. Furthermore, the current industrial structure, with its reliance on traditional industries, may hinder the optimization of logistics systems. Based on these results, several policy recommendations are put forward, including the optimization of the industrial structure, better integration of information technologies in logistics processes, and the strategic utilization of Sichuan’s geographical advantages. This research provides valuable insights for policymakers aiming to enhance logistics efficiency as part of the region’s broader economic development strategy. ]]> An Empirical Analysis of Regional Logistics Efficiency and Its Determinants in Sichuan Province: Evidence from DEA and Tobit Models hong tang shasha yu xiaowen sun doi: 10.56578/atams020303 Acadlore Transactions on Applied Mathematics and Statistics 09-29-2024 Acadlore Transactions on Applied Mathematics and Statistics 09-29-2024 2024 2 3 Article 150 10.56578/atams020303 https://www.acadlore.com/article/ATAMS/2024_2_3/atams020303 https://www.acadlore.com/article/ATAMS/2024_2_3/atams020302 The incorporation of fractional calculus into nanofluid models has proven effective in capturing the complex dynamics of nanofluid flow and heat transfer, thereby enhancing the precision of predictions in this intricate field. In this study, the dynamics of a viscoelastic second-grade nanofluid model are examined through the application of the Laplace transform technique on a vertical plate. Initially, the model is formulated as coupled partial differential equations to describe the second-grade nanofluid system. The governing equations are then rendered dimensionless using appropriate dimensionless parameters. The non-dimensional model is subsequently generalized by introducing a modified Caputo fractional derivative operator. To model a homogenous nanofluid, nanoparticles of $\mathrm{Al}_2 \mathrm{O}_3$ in nanometer-sized form are suspended in mineral transformer oil. The Laplace transform is employed to solve the momentum, energy, and mass diffusion equations, providing analytical solutions. Graphical and tabular analyses are conducted to assess the influence of various physical parameters—including the fractional order, nanoparticle volume fraction, and time parameter—on the velocity, thermal, and concentration profiles. The results indicate that increasing the nanoparticle volume fraction, fractional order, and time parameter significantly enhances the rate of heat transfer. Additionally, it is observed that the velocity, temperature, and concentration profiles are notably affected by increasing the volume fraction of nanoparticles. The accuracy and reliability of the obtained solutions are validated through comparisons with existing literature. This work advances the understanding of nanofluid dynamics and presents valuable insights for industrial applications, particularly in enhancing heat transfer performance. 09-29-2024 <![CDATA[ <p>The incorporation of fractional calculus into nanofluid models has proven effective in capturing the complex dynamics of nanofluid flow and heat transfer, thereby enhancing the precision of predictions in this intricate field. In this study, the dynamics of a viscoelastic second-grade nanofluid model are examined through the application of the Laplace transform technique on a vertical plate. Initially, the model is formulated as coupled partial differential equations to describe the second-grade nanofluid system. The governing equations are then rendered dimensionless using appropriate dimensionless parameters. The non-dimensional model is subsequently generalized by introducing a modified Caputo fractional derivative operator. To model a homogenous nanofluid, nanoparticles of $\mathrm{Al}_2 \mathrm{O}_3$ in nanometer-sized form are suspended in mineral transformer oil. The Laplace transform is employed to solve the momentum, energy, and mass diffusion equations, providing analytical solutions. Graphical and tabular analyses are conducted to assess the influence of various physical parameters—including the fractional order, nanoparticle volume fraction, and time parameter—on the velocity, thermal, and concentration profiles. The results indicate that increasing the nanoparticle volume fraction, fractional order, and time parameter significantly enhances the rate of heat transfer. Additionally, it is observed that the velocity, temperature, and concentration profiles are notably affected by increasing the volume fraction of nanoparticles. The accuracy and reliability of the obtained solutions are validated through comparisons with existing literature. This work advances the understanding of nanofluid dynamics and presents valuable insights for industrial applications, particularly in enhancing heat transfer performance.</p> ]]> Application of Laplace Transform Technique of Variable Order to the Generalized Caputo Fractional Model of Second Grade Nanofluid zubair ahmad saqib murtaza razi khan doi: 10.56578/atams020302 Acadlore Transactions on Applied Mathematics and Statistics 09-29-2024 Acadlore Transactions on Applied Mathematics and Statistics 09-29-2024 2024 2 3 Article 133 10.56578/atams020302 https://www.acadlore.com/article/ATAMS/2024_2_3/atams020302 https://www.acadlore.com/article/ATAMS/2024_2_3/atams020301 This work aims to apply the spherical fuzzy set (SFS), a flexible framework for handling ambiguous human opinions, to improve decision-making processes in recycled water. It specifically looks at the application of Sugeno-Weber (SW) triangular norms in the spherical fuzzy (SF) information domain, providing reliable approximations that are necessary for decision-making. A new class of aggregation operators is presented in this paper. These operators are specifically made for spherical fuzzy information systems and include the interval value spherical fuzzy Sugeno–Weber power weighted average (IVSFSWPA), interval value spherical fuzzy Sugeno–Weber power geometric (IVSFSWPWG), and interval value spherical fuzzy Sugeno–Weber power weighted average (IVSFSWPWA). The realistic features and special cases of these operators are demonstrated, highlighting how well they fit into practical scenarios. A new method for multi-attribute decision-making (MADM) is used for a range of real-world applications with different requirements or characteristics. The efficacy of the recommended methodologies is demonstrated with an example of a recycled water selection process. Additionally, a thorough comparison method is provided to show how the suggested aggregation strategies work and are relevant by contrasting their results with those of the current methods. The study's conclusion highlights the potential contribution of the recommended research to the advancement of decision-making techniques in dynamic and complex environments. It also summarizes its findings and discusses its prospects moving forward. 09-24-2024 <![CDATA[ This work aims to apply the spherical fuzzy set (SFS), a flexible framework for handling ambiguous human opinions, to improve decision-making processes in recycled water. It specifically looks at the application of Sugeno-Weber (SW) triangular norms in the spherical fuzzy (SF) information domain, providing reliable approximations that are necessary for decision-making. A new class of aggregation operators is presented in this paper. These operators are specifically made for spherical fuzzy information systems and include the interval value spherical fuzzy Sugeno–Weber power weighted average (IVSFSWPA), interval value spherical fuzzy Sugeno–Weber power geometric (IVSFSWPWG), and interval value spherical fuzzy Sugeno–Weber power weighted average (IVSFSWPWA). The realistic features and special cases of these operators are demonstrated, highlighting how well they fit into practical scenarios. A new method for multi-attribute decision-making (MADM) is used for a range of real-world applications with different requirements or characteristics. The efficacy of the recommended methodologies is demonstrated with an example of a recycled water selection process. Additionally, a thorough comparison method is provided to show how the suggested aggregation strategies work and are relevant by contrasting their results with those of the current methods. The study's conclusion highlights the potential contribution of the recommended research to the advancement of decision-making techniques in dynamic and complex environments. It also summarizes its findings and discusses its prospects moving forward. ]]> Using Sugeno-Weber Triangular Norm-Based Interval Value Spherical Fuzzy Information for Recycled Water mehwish sarfarz darko božanić doi: 10.56578/atams020301 Acadlore Transactions on Applied Mathematics and Statistics 09-24-2024 Acadlore Transactions on Applied Mathematics and Statistics 09-24-2024 2024 2 3 Article 117 10.56578/atams020301 https://www.acadlore.com/article/ATAMS/2024_2_3/atams020301 https://www.acadlore.com/article/ATAMS/2024_2_2/atams020205 In the present work we investigate the collapsing and expanding solutions of the Einstein's field equation of anisotropic fluid in spherically symmetric space-time and with charge within the framework of ${f(R, T)}$ theory, where $R$ denotes the Ricci scalar and $T$ denotes the trace of the energy$-$momentum tensor. We also evaluate the expansion scalar, whose negative values result in collapse and positive values yield expansion. We analyzed the impacts of charge in ${f(R, T)}$ theory on the density and pressure distribution of the collapsing and expanding fluid and noticed the involvement of anisotropic fluid in the process of collapsing and expanding with charge in $ {f(R, T)}$. Furthermore, the definition of mass function has been used to analyse the condition for the trapped surface, and it has been found that in this case there is only one horizon. In all scenarios, the effects of coupling parameters $\lambda$ and $q$ have been thoroughly examined. Additionally, we have created graphs representing pressures, anisotropy, and energy density in ${f(R, T)}$ theory and check the effect of charge on these quantities. 06-29-2024 <![CDATA[ <p>In the present work we investigate the collapsing and expanding solutions of the Einstein's field equation of anisotropic fluid in spherically symmetric space-time and with charge within the framework of ${f(R, T)}$ theory, where $R$ denotes the Ricci scalar and $T$ denotes the trace of the energy$-$momentum tensor. We also evaluate the expansion scalar, whose negative values result in collapse and positive values yield expansion. We analyzed the impacts of charge in ${f(R, T)}$ theory on the density and pressure distribution of the collapsing and expanding fluid and noticed the involvement of anisotropic fluid in the process of collapsing and expanding with charge in $ {f(R, T)}$. Furthermore, the definition of mass function has been used to analyse the condition for the trapped surface, and it has been found that in this case there is only one horizon. In all scenarios, the effects of coupling parameters $\lambda$ and $q$ have been thoroughly examined. Additionally, we have created graphs representing pressures, anisotropy, and energy density in ${f(R, T)}$ theory and check the effect of charge on these quantities.</p> ]]> Collapsing and Expanding Observation of Anisotropic Charged Source in ${f(R, T)}$ Gravity jan muhammad rifaqat ali doi: 10.56578/atams020205 Acadlore Transactions on Applied Mathematics and Statistics 06-29-2024 Acadlore Transactions on Applied Mathematics and Statistics 06-29-2024 2024 2 2 Article 104 10.56578/atams020205 https://www.acadlore.com/article/ATAMS/2024_2_2/atams020205 https://www.acadlore.com/article/ATAMS/2024_2_2/atams020204 Food inflation presents a significant challenge in Nigeria. This study examines the volatility of four primary food items—tomatoes, yam, yellow garri, and imported rice—in Cross River State, Nigeria, utilizing data on monthly retail prices per kilogram from January 1997 to November 2023, sourced from the National Bureau of Statistics (NBS). Three asymmetric volatility models were employed: Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH), Threshold Autoregressive Conditional Heteroscedasticity (TARCH), and Power Autoregressive Conditional Heteroscedasticity (PARCH). The parameters of these models were estimated using three distributions of error innovations: Normal, Student's t-distribution, and Generalized Error Distribution (GED). The performance of the models was assessed based on log-likelihood for fitness and Root Mean Square Error (RMSE) for forecasting accuracy. The results indicated that non-Gaussian error innovations outperformed the normal distribution. Notably, higher persistence in volatility was observed for yam and tomatoes compared to yellow garri and imported rice. Tomatoes exhibited the highest volatility persistence among the food items analyzed. Significant Generalized Autoregressive Conditional Heteroscedasticity (GARCH) terms for tomatoes and yam suggested that past volatility has a significant positive impact on their current volatility, whereas this effect was not significant for yellow garri and imported rice (p$<$0.05). The leverage effect was found to be insignificant, indicating that positive and negative shocks in volatility exert similar effects on the volatility of these food items. These findings underscore the urgent need for incentives and adequate security measures to ensure food sufficiency in Cross River State and Nigeria at large. 06-27-2024 <![CDATA[ Food inflation presents a significant challenge in Nigeria. This study examines the volatility of four primary food items—tomatoes, yam, yellow garri, and imported rice—in Cross River State, Nigeria, utilizing data on monthly retail prices per kilogram from January 1997 to November 2023, sourced from the National Bureau of Statistics (NBS). Three asymmetric volatility models were employed: Exponential Generalized Autoregressive Conditional Heteroscedasticity (EGARCH), Threshold Autoregressive Conditional Heteroscedasticity (TARCH), and Power Autoregressive Conditional Heteroscedasticity (PARCH). The parameters of these models were estimated using three distributions of error innovations: Normal, Student's t-distribution, and Generalized Error Distribution (GED). The performance of the models was assessed based on log-likelihood for fitness and Root Mean Square Error (RMSE) for forecasting accuracy. The results indicated that non-Gaussian error innovations outperformed the normal distribution. Notably, higher persistence in volatility was observed for yam and tomatoes compared to yellow garri and imported rice. Tomatoes exhibited the highest volatility persistence among the food items analyzed. Significant Generalized Autoregressive Conditional Heteroscedasticity (GARCH) terms for tomatoes and yam suggested that past volatility has a significant positive impact on their current volatility, whereas this effect was not significant for yellow garri and imported rice (p$<$0.05). The leverage effect was found to be insignificant, indicating that positive and negative shocks in volatility exert similar effects on the volatility of these food items. These findings underscore the urgent need for incentives and adequate security measures to ensure food sufficiency in Cross River State and Nigeria at large. ]]> Modeling Retail Price Volatility of Selected Food Items in Cross River State, Nigeria Using GARCH Models nkoyo abednego essien chikadibia alfred umah lgbo-anozie uloma amarachi timothy kayode samson doi: 10.56578/atams020204 Acadlore Transactions on Applied Mathematics and Statistics 06-27-2024 Acadlore Transactions on Applied Mathematics and Statistics 06-27-2024 2024 2 2 Article 94 10.56578/atams020204 https://www.acadlore.com/article/ATAMS/2024_2_2/atams020204 https://www.acadlore.com/article/ATAMS/2024_2_2/atams020203 This investigation was conducted to assess the impact of effort, interest, and cognitive competence on statistics achievement, mediated by self-concept among students. The study engaged 453 students enrolled in a statistics course at Yarmouk University, Jordan, who completed a self-report questionnaire. Path analysis facilitated the examination of both direct and indirect influences exerted by effort, interest, and cognitive competence on statistics achievement, with self-concept serving as a mediator. It was found that effort, interest, and cognitive competence significantly directly affected statistics achievement. Furthermore, self-concept was observed to partially mediate the relationships between each of effort, interest, cognitive competence, and statistics achievement. These results underscore the critical roles of effort, interest, and cognitive competence as predictors of success in statistics. The partial mediation by self-concept suggests its important but not exclusive role in enhancing academic outcomes. This study contributes to educational strategies by highlighting the potential of interventions focused on self-concept enhancement to improve academic performance in statistical education. Implications for educators and policy-makers are discussed in terms of designing effective educational interventions. 05-13-2024 <![CDATA[ This investigation was conducted to assess the impact of effort, interest, and cognitive competence on statistics achievement, mediated by self-concept among students. The study engaged 453 students enrolled in a statistics course at Yarmouk University, Jordan, who completed a self-report questionnaire. Path analysis facilitated the examination of both direct and indirect influences exerted by effort, interest, and cognitive competence on statistics achievement, with self-concept serving as a mediator. It was found that effort, interest, and cognitive competence significantly directly affected statistics achievement. Furthermore, self-concept was observed to partially mediate the relationships between each of effort, interest, cognitive competence, and statistics achievement. These results underscore the critical roles of effort, interest, and cognitive competence as predictors of success in statistics. The partial mediation by self-concept suggests its important but not exclusive role in enhancing academic outcomes. This study contributes to educational strategies by highlighting the potential of interventions focused on self-concept enhancement to improve academic performance in statistical education. Implications for educators and policy-makers are discussed in terms of designing effective educational interventions. ]]> Analyzing Impact of Effort, Interest and Cognitive-Competence on Statistics Achievement Through Meditation of Self-Concept Statistics manar hazaimeh abdullah m. al-ansi jebril al-hrinat ghadeer adwan aseel hendi doi: 10.56578/atams020203 Acadlore Transactions on Applied Mathematics and Statistics 05-13-2024 Acadlore Transactions on Applied Mathematics and Statistics 05-13-2024 2024 2 2 Article 81 10.56578/atams020203 https://www.acadlore.com/article/ATAMS/2024_2_2/atams020203 https://www.acadlore.com/article/ATAMS/2024_2_2/atams020202 In this study, an extensive examination of topological parameters derived from molecular structures is conducted, with a specific focus on the Randic index, Geometric Arithmetic (GA) index, and Atom Bond Connectivity (ABC) index. These indices are applied to concealed non-Kekulean benzenoids and subdivided networks within line graphs. The investigation reveals patterns and relationships that were previously unexplored, shedding light on the structural intricacies of chemical compounds. The utility of graph theory as an effective tool for modeling and designing interconnection devices within the realm of chemical research is underscored. Such an approach not only advances the field of mathematical chemistry but also enriches understanding of the manipulation of chemical structures for extensive scientific applications. This analysis contributes to the body of knowledge by highlighting the relevance of these indices in unveiling complex molecular topologies and their potential implications for theoretical and applied chemistry. 04-29-2024 <![CDATA[ In this study, an extensive examination of topological parameters derived from molecular structures is conducted, with a specific focus on the Randic index, Geometric Arithmetic (GA) index, and Atom Bond Connectivity (ABC) index. These indices are applied to concealed non-Kekulean benzenoids and subdivided networks within line graphs. The investigation reveals patterns and relationships that were previously unexplored, shedding light on the structural intricacies of chemical compounds. The utility of graph theory as an effective tool for modeling and designing interconnection devices within the realm of chemical research is underscored. Such an approach not only advances the field of mathematical chemistry but also enriches understanding of the manipulation of chemical structures for extensive scientific applications. This analysis contributes to the body of knowledge by highlighting the relevance of these indices in unveiling complex molecular topologies and their potential implications for theoretical and applied chemistry. ]]> A Mathematical Analysis of Concealed Non-Kekulean Benzenoids and Subdivided Networks in Associated Line Graphs nasir ali zaeema kousar maimoona safdar javeria safdar fikadu tesgera tolasa doi: 10.56578/atams020202 Acadlore Transactions on Applied Mathematics and Statistics 04-29-2024 Acadlore Transactions on Applied Mathematics and Statistics 04-29-2024 2024 2 2 Article 72 10.56578/atams020202 https://www.acadlore.com/article/ATAMS/2024_2_2/atams020202 https://www.acadlore.com/article/ATAMS/2024_2_2/atams020201 In the pursuit of advancing multi-attribute group decision-making (MAGDM) methodologies, this study introduces two novel aggregation operators: the Induced Confidence Complex Pythagorean Fuzzy Ordered Weighted Geometric Aggregation (ICCPyFOWGA) operator and the Induced Confidence Complex Pythagorean Fuzzy Hybrid Geometric Aggregation (ICCPyFHGA) operator. These operators are characterized by their capacity to integrate various decision criteria based on complex Pythagorean fuzzy sets (CPyFSs), with an emphasis on the influence of confidence levels. Key structural properties of these operators, such as idempotency, boundedness, and monotonicity, are rigorously established. Furthermore, the practical applicability of these models in real-world decision-making scenarios is demonstrated through a descriptive example that underscores their efficiency and effectiveness. The analytical results affirm that the proposed operators not only enhance decision-making precision but also offer a flexible framework for addressing diverse decision-making environments. This contribution marks a significant advancement in the field of decision science, providing a robust tool for experts and practitioners involved in complex decision-making processes. 04-28-2024 <![CDATA[ In the pursuit of advancing multi-attribute group decision-making (MAGDM) methodologies, this study introduces two novel aggregation operators: the Induced Confidence Complex Pythagorean Fuzzy Ordered Weighted Geometric Aggregation (ICCPyFOWGA) operator and the Induced Confidence Complex Pythagorean Fuzzy Hybrid Geometric Aggregation (ICCPyFHGA) operator. These operators are characterized by their capacity to integrate various decision criteria based on complex Pythagorean fuzzy sets (CPyFSs), with an emphasis on the influence of confidence levels. Key structural properties of these operators, such as idempotency, boundedness, and monotonicity, are rigorously established. Furthermore, the practical applicability of these models in real-world decision-making scenarios is demonstrated through a descriptive example that underscores their efficiency and effectiveness. The analytical results affirm that the proposed operators not only enhance decision-making precision but also offer a flexible framework for addressing diverse decision-making environments. This contribution marks a significant advancement in the field of decision science, providing a robust tool for experts and practitioners involved in complex decision-making processes. ]]> Efficacy of Induced Complex Aggregation Operators in Multi-Attribute Decision-Making with Confidence Levels quaid iqbal zia ullah khan doi: 10.56578/atams020201 Acadlore Transactions on Applied Mathematics and Statistics 04-28-2024 Acadlore Transactions on Applied Mathematics and Statistics 04-28-2024 2024 2 2 Article 64 10.56578/atams020201 https://www.acadlore.com/article/ATAMS/2024_2_2/atams020201 https://www.acadlore.com/article/ATAMS/2024_2_1/atams020105 In the field of graph theory, the exploration of connectivity patterns within various graph families is paramount. This study is dedicated to the examination of the neighbourhood degree-based topological index, a quantitative measure devised to elucidate the structural complexities inherent in diverse graph families. An initial overview of existing topological indices sets the stage for the introduction of the mathematical formulation and theoretical underpinnings of the neighbourhood degree-based index. Through meticulous analysis, the efficacy of this index in delineating unique connectivity patterns and structural characteristics across graph families is demonstrated. The utility of the neighbourhood degree-based index extends beyond theoretical graph theory, finding applicability in network science, chemistry, and social network analysis, thereby underscoring its interdisciplinary relevance. By offering a novel perspective on topological indices and their role in deciphering complex network structures, this research makes a significant contribution to the advancement of graph theory. The findings not only underscore the versatility of the neighbourhood degree-based topological index but also highlight its potential as a tool for understanding connectivity patterns in a wide array of contexts. This comprehensive analysis not only enriches the theoretical landscape of graph descriptors but also paves the way for practical applications in various scientific domains, illustrating the profound impact of graph theoretical studies on understanding the intricacies of networked systems. 02-04-2024 <![CDATA[ In the field of graph theory, the exploration of connectivity patterns within various graph families is paramount. This study is dedicated to the examination of the neighbourhood degree-based topological index, a quantitative measure devised to elucidate the structural complexities inherent in diverse graph families. An initial overview of existing topological indices sets the stage for the introduction of the mathematical formulation and theoretical underpinnings of the neighbourhood degree-based index. Through meticulous analysis, the efficacy of this index in delineating unique connectivity patterns and structural characteristics across graph families is demonstrated. The utility of the neighbourhood degree-based index extends beyond theoretical graph theory, finding applicability in network science, chemistry, and social network analysis, thereby underscoring its interdisciplinary relevance. By offering a novel perspective on topological indices and their role in deciphering complex network structures, this research makes a significant contribution to the advancement of graph theory. The findings not only underscore the versatility of the neighbourhood degree-based topological index but also highlight its potential as a tool for understanding connectivity patterns in a wide array of contexts. This comprehensive analysis not only enriches the theoretical landscape of graph descriptors but also paves the way for practical applications in various scientific domains, illustrating the profound impact of graph theoretical studies on understanding the intricacies of networked systems. ]]> Neighbourhood Degree-Based Graph Descriptors: A Comprehensive Analysis of Connectivity Patterns in Diverse Graph Families and Their Applicapability abdu alameri abid mahboob emad toma karash doi: 10.56578/atams020105 Acadlore Transactions on Applied Mathematics and Statistics 02-04-2024 Acadlore Transactions on Applied Mathematics and Statistics 02-04-2024 2024 2 1 Article 52 10.56578/atams020105 https://www.acadlore.com/article/ATAMS/2024_2_1/atams020105 https://www.acadlore.com/article/ATAMS/2024_2_1/atams020104 Inducing variables are the parameters or conditions that influence the membership value of an element in a fuzzy set. These variables are often linguistic in nature and represent qualitative aspects of the problem. Thus, the objective of this paper is introduce some aggregation operators based on inducing variable, such as induced complex Polytopic fuzzy ordered weighted averaging aggregation operator (I-CPoFOWAAO) and induced complex Polytopic fuzzy hybrid averaging aggregation operator (I-CPoFHAAO). Induced aggregation operators in decision-making process are indispensable tools for managing uncertainty, integrating multiple criteria, facilitating consensus, and providing a formal and flexible framework for modeling and solving complex decision problems. At the end of the paper, we make an illustrative example to prove the ability and efficiency of the novel proposed aggregation operators. 02-03-2024 <![CDATA[ Inducing variables are the parameters or conditions that influence the membership value of an element in a fuzzy set. These variables are often linguistic in nature and represent qualitative aspects of the problem. Thus, the objective of this paper is introduce some aggregation operators based on inducing variable, such as induced complex Polytopic fuzzy ordered weighted averaging aggregation operator (I-CPoFOWAAO) and induced complex Polytopic fuzzy hybrid averaging aggregation operator (I-CPoFHAAO). Induced aggregation operators in decision-making process are indispensable tools for managing uncertainty, integrating multiple criteria, facilitating consensus, and providing a formal and flexible framework for modeling and solving complex decision problems. At the end of the paper, we make an illustrative example to prove the ability and efficiency of the novel proposed aggregation operators. ]]> Complex Polytopic Fuzzy Model and Their Induced Aggregation Operators khaista rahman jan muhammad doi: 10.56578/atams020104 Acadlore Transactions on Applied Mathematics and Statistics 02-03-2024 Acadlore Transactions on Applied Mathematics and Statistics 02-03-2024 2024 2 1 Article 42 10.56578/atams020104 https://www.acadlore.com/article/ATAMS/2024_2_1/atams020104 https://www.acadlore.com/article/ATAMS/2024_2_1/atams020103 In this investigation, the exact formulas for geometric-harmonic (GH), neighborhood geometric-harmonic (NGH), harmonic-geometric (HG), and neighborhood harmonic-geometric (NHG) indices were systematically evaluated for hyaluronic acid-curcumin (HAC) and hyaluronic acid-paclitaxel (HAP) conjugates. Through this evaluation, a comprehensive quantitative assessment was conducted to elucidate the structural characteristics of these conjugates, highlighting the intricate geometric and harmonic relationships present within their molecular graphs. The study leveraged these indices to illuminate the complex interplay between geometric and harmonic properties, providing a novel perspective on the molecular architecture of HAC and HAP conjugates. This analytical approach not only sheds light on the structural nuances of these compounds but also offers a unique lens through which their potential in drug delivery applications can be assessed. Graphical analyses of the results further enhance the understanding of these molecular properties, presenting a detailed visualization that complements the quantitative findings. The integration of these topological descriptors into the study of HAC and HAP conjugates represents a significant advance in the field of medicinal chemistry, offering valuable insights for researchers engaged in the development of innovative drug delivery systems. The findings underscore the utility of these descriptors in characterizing the molecular topology of complex conjugates, setting the stage for further exploration of their applications in therapeutic contexts. 02-02-2024 <![CDATA[ In this investigation, the exact formulas for geometric-harmonic (GH), neighborhood geometric-harmonic (NGH), harmonic-geometric (HG), and neighborhood harmonic-geometric (NHG) indices were systematically evaluated for hyaluronic acid-curcumin (HAC) and hyaluronic acid-paclitaxel (HAP) conjugates. Through this evaluation, a comprehensive quantitative assessment was conducted to elucidate the structural characteristics of these conjugates, highlighting the intricate geometric and harmonic relationships present within their molecular graphs. The study leveraged these indices to illuminate the complex interplay between geometric and harmonic properties, providing a novel perspective on the molecular architecture of HAC and HAP conjugates. This analytical approach not only sheds light on the structural nuances of these compounds but also offers a unique lens through which their potential in drug delivery applications can be assessed. Graphical analyses of the results further enhance the understanding of these molecular properties, presenting a detailed visualization that complements the quantitative findings. The integration of these topological descriptors into the study of HAC and HAP conjugates represents a significant advance in the field of medicinal chemistry, offering valuable insights for researchers engaged in the development of innovative drug delivery systems. The findings underscore the utility of these descriptors in characterizing the molecular topology of complex conjugates, setting the stage for further exploration of their applications in therapeutic contexts. ]]> Exploring Novel Topological Descriptors: Geometric-Harmonic and Harmonic-Geometric Descriptors for HAC and HAP Conjugates ali raza fikadu tesgera tolasa doi: 10.56578/atams020103 Acadlore Transactions on Applied Mathematics and Statistics 02-02-2024 Acadlore Transactions on Applied Mathematics and Statistics 02-02-2024 2024 2 1 Article 32 10.56578/atams020103 https://www.acadlore.com/article/ATAMS/2024_2_1/atams020103 https://www.acadlore.com/article/ATAMS/2024_2_1/atams020102 This study introduces an advanced framework for picture fuzzy linear programming problems (PFLPP), deploying picture fuzzy numbers (PFNs) to articulate diverse parameters. Integral to this approach are the three cardinal membership functions: membership, neutral, and non-membership, each contributing distinctly to the formation of the PFLPP. Emphasis is placed on employing these degrees to formulate the PFLPP in its most unadulterated form. Furthermore, the research delineates a novel optimization model, tailored specifically for the resolution of the PFLPP. A meticulous case study, accompanied by a numerical example, is presented, demonstrating the efficacy and robustness of the proposed methodology. The study culminates in a comprehensive discussion of the findings, highlighting pivotal insights and delineating potential avenues for future inquiry. This exploration not only advances the theoretical underpinnings of picture fuzzy sets but also offers practical implications for the application of linear programming in complex decision-making scenarios. 01-24-2024 <![CDATA[ This study introduces an advanced framework for picture fuzzy linear programming problems (PFLPP), deploying picture fuzzy numbers (PFNs) to articulate diverse parameters. Integral to this approach are the three cardinal membership functions: membership, neutral, and non-membership, each contributing distinctly to the formation of the PFLPP. Emphasis is placed on employing these degrees to formulate the PFLPP in its most unadulterated form. Furthermore, the research delineates a novel optimization model, tailored specifically for the resolution of the PFLPP. A meticulous case study, accompanied by a numerical example, is presented, demonstrating the efficacy and robustness of the proposed methodology. The study culminates in a comprehensive discussion of the findings, highlighting pivotal insights and delineating potential avenues for future inquiry. This exploration not only advances the theoretical underpinnings of picture fuzzy sets but also offers practical implications for the application of linear programming in complex decision-making scenarios. ]]> Picture Fuzzy Linear Programming Problems chiranjibe jana zdravko nunić doi: 10.56578/atams020102 Acadlore Transactions on Applied Mathematics and Statistics 01-24-2024 Acadlore Transactions on Applied Mathematics and Statistics 01-24-2024 2024 2 1 Article 22 10.56578/atams020102 https://www.acadlore.com/article/ATAMS/2024_2_1/atams020102 https://www.acadlore.com/article/ATAMS/2024_2_1/atams020101 In the realm of decision-making, the delineation of uncertainty and ambiguity within data is a pivotal challenge. This study introduces a novel approach through complex intuitive hesitant fuzzy sets (CIHFS), which offers a unique multidimensional perspective for data analysis. The CIHFS framework is predicated on the concept that membership degrees reside within the unit disc of the complex plane, thereby providing a more nuanced representation of data. This method stands apart in its ability to simultaneously process and analyze data in a two-dimensional format, incorporating additional descriptive elements known as phase terms into the membership degrees. The study is bifurcated into two primary phases. Initially, a possibility degree measure is proposed, facilitating the ranking of numerical values within the CIHFS context. Subsequently, the development of innovative operational rules and aggregation operators (AOs) is undertaken. These AOs are instrumental in amalgamating diverse options within a CIHFS framework. The research dissects and deliberates on various AOs, including weighted average (WA), ordered weighted average (OWA), weighted geometric (WG), ordered weighted geometric (OWG), hybrid average (HA), and hybrid geometric (HG). Furthermore, the study extends to the realm of multi-criteria decision making (MCDM), where it proposes a methodology utilizing intricate intuitive and fuzzy information. This methodology emphasizes the objective management of weights, thereby enhancing the decision-making process. The study's findings hold significant implications for the optimization of resources and decision-making strategies, providing a robust framework for the application of CIHFS in practical scenarios. 01-15-2024 <![CDATA[ In the realm of decision-making, the delineation of uncertainty and ambiguity within data is a pivotal challenge. This study introduces a novel approach through complex intuitive hesitant fuzzy sets (CIHFS), which offers a unique multidimensional perspective for data analysis. The CIHFS framework is predicated on the concept that membership degrees reside within the unit disc of the complex plane, thereby providing a more nuanced representation of data. This method stands apart in its ability to simultaneously process and analyze data in a two-dimensional format, incorporating additional descriptive elements known as phase terms into the membership degrees. The study is bifurcated into two primary phases. Initially, a possibility degree measure is proposed, facilitating the ranking of numerical values within the CIHFS context. Subsequently, the development of innovative operational rules and aggregation operators (AOs) is undertaken. These AOs are instrumental in amalgamating diverse options within a CIHFS framework. The research dissects and deliberates on various AOs, including weighted average (WA), ordered weighted average (OWA), weighted geometric (WG), ordered weighted geometric (OWG), hybrid average (HA), and hybrid geometric (HG). Furthermore, the study extends to the realm of multi-criteria decision making (MCDM), where it proposes a methodology utilizing intricate intuitive and fuzzy information. This methodology emphasizes the objective management of weights, thereby enhancing the decision-making process. The study's findings hold significant implications for the optimization of resources and decision-making strategies, providing a robust framework for the application of CIHFS in practical scenarios. ]]> Complex Intuitionistic Hesitant Fuzzy Aggregation Information and Their Application in Decision Making Problems muhammad ahmed shahzaib ashraf daoud suleiman mashat doi: 10.56578/atams020101 Acadlore Transactions on Applied Mathematics and Statistics 01-15-2024 Acadlore Transactions on Applied Mathematics and Statistics 01-15-2024 2024 2 1 Article 1 10.56578/atams020101 https://www.acadlore.com/article/ATAMS/2024_2_1/atams020101 https://www.acadlore.com/article/ATAMS/2023_1_3/atams010305 In the realm of epidemiological modeling, the intricacies of epidemic dynamics are elucidated through the lens of compartmental models, with the SIR (Susceptible-Infectious-Recovered) and its variant, the SIS (Susceptible-Infectious-Susceptible) model, being pivotal. This investigation delves into both deterministic and stochastic frameworks, casting the SIR model as a continuous-time Markov chain (CTMC) in stochastic settings. Such an approach facilitates simulations via Gillespie's algorithm and integration of stochastic differential equations. The latter are formulated through a bivariate Fokker-Planck equation, originating from the continuous limit of the master equation. A focal point of this study is the distribution of extinction time, specifically, the duration until recovery in a population with an initial count of infected individuals. This distribution adheres to a Gumbel distribution, viewed through the prism of a birth and death process. The stochastic analysis reveals several insights: firstly, the SIR model as a CTMC encapsulates random fluctuations in epidemic dynamics. Secondly, stochastic simulation methods, either through Gillespie's algorithm or stochastic differential equations, offer a robust exploration of disease spread variability. Thirdly, the precision of modeling is enhanced by the incorporation of a bivariate Fokker-Planck equation. Fourthly, understanding the Gumbel distribution of extinction time is crucial for gauging recovery periods. Lastly, the non-linear nature of the SIR model, when analyzed stochastically, enriches the comprehension of epidemic dynamics. These findings bear significant implications for epidemic mitigation and recovery strategies, informing healthcare resource planning, vaccine deployment optimization, implementation of social distancing measures, public communication strategies, and swift responses to epidemic resurgences. 12-30-2023 <![CDATA[ In the realm of epidemiological modeling, the intricacies of epidemic dynamics are elucidated through the lens of compartmental models, with the SIR (Susceptible-Infectious-Recovered) and its variant, the SIS (Susceptible-Infectious-Susceptible) model, being pivotal. This investigation delves into both deterministic and stochastic frameworks, casting the SIR model as a continuous-time Markov chain (CTMC) in stochastic settings. Such an approach facilitates simulations via Gillespie's algorithm and integration of stochastic differential equations. The latter are formulated through a bivariate Fokker-Planck equation, originating from the continuous limit of the master equation. A focal point of this study is the distribution of extinction time, specifically, the duration until recovery in a population with an initial count of infected individuals. This distribution adheres to a Gumbel distribution, viewed through the prism of a birth and death process. The stochastic analysis reveals several insights: firstly, the SIR model as a CTMC encapsulates random fluctuations in epidemic dynamics. Secondly, stochastic simulation methods, either through Gillespie's algorithm or stochastic differential equations, offer a robust exploration of disease spread variability. Thirdly, the precision of modeling is enhanced by the incorporation of a bivariate Fokker-Planck equation. Fourthly, understanding the Gumbel distribution of extinction time is crucial for gauging recovery periods. Lastly, the non-linear nature of the SIR model, when analyzed stochastically, enriches the comprehension of epidemic dynamics. These findings bear significant implications for epidemic mitigation and recovery strategies, informing healthcare resource planning, vaccine deployment optimization, implementation of social distancing measures, public communication strategies, and swift responses to epidemic resurgences. ]]> Stochastic Dynamics and Extinction Time in SIR Epidemiological Models rachid el chaal said bouchefra moulay othman aboutafail doi: 10.56578/atams010305 Acadlore Transactions on Applied Mathematics and Statistics 12-30-2023 Acadlore Transactions on Applied Mathematics and Statistics 12-30-2023 2023 1 3 Article 181 10.56578/atams010305 https://www.acadlore.com/article/ATAMS/2023_1_3/atams010305 https://www.acadlore.com/article/ATAMS/2023_1_3/atams010304 In the realm of emergency response, where time and information constraints are paramount, and scenarios often involve high levels of toxicity and uncertainty, the effective management of industrial control systems (ICS) is critical. This study introduces novel methodologies for enhancing decision-making processes in emergency situations, specifically focusing on ICS-security. Central to this research is the employment of spherical hesitant fuzzy soft set (SHFSS), a concept that thrives in the presence of ambiguity and incomplete information. The research adopts and extends the parametric families of t-norms and t-conorms, as introduced by Yager, to analyze these sets. This approach is instrumental in addressing multi-attribute decision-making (MADM) problems within the ICS-security domain. To this end, four distinct aggregation operators (AOs) are proposed: spherical hesitant fuzzy soft yager weighted averaging aggregation, spherical hesitant fuzzy soft yager ordered weighted averaging aggregation, spherical hesitant fuzzy soft yager weighted geometric aggregation, and spherical hesitant fuzzy soft yager ordered weighted geometric aggregation. These operators are tailored to harness the operational benefits of Yager's parametric families, thereby offering a robust framework for dealing with decision-making problems under uncertainty. Further, an algorithm specifically designed for MADM is presented, which integrates these AOs. The efficacy and precision of the proposed methodology are demonstrated through a numerical example, applied in the context of an ICS security supplier. This example serves as a testament to the superiority of the approach in handling complex decision-making scenarios inherent in ICS-security management. 12-12-2023 <![CDATA[ In the realm of emergency response, where time and information constraints are paramount, and scenarios often involve high levels of toxicity and uncertainty, the effective management of industrial control systems (ICS) is critical. This study introduces novel methodologies for enhancing decision-making processes in emergency situations, specifically focusing on ICS-security. Central to this research is the employment of spherical hesitant fuzzy soft set (SHFSS), a concept that thrives in the presence of ambiguity and incomplete information. The research adopts and extends the parametric families of t-norms and t-conorms, as introduced by Yager, to analyze these sets. This approach is instrumental in addressing multi-attribute decision-making (MADM) problems within the ICS-security domain. To this end, four distinct aggregation operators (AOs) are proposed: spherical hesitant fuzzy soft yager weighted averaging aggregation, spherical hesitant fuzzy soft yager ordered weighted averaging aggregation, spherical hesitant fuzzy soft yager weighted geometric aggregation, and spherical hesitant fuzzy soft yager ordered weighted geometric aggregation. These operators are tailored to harness the operational benefits of Yager's parametric families, thereby offering a robust framework for dealing with decision-making problems under uncertainty. Further, an algorithm specifically designed for MADM is presented, which integrates these AOs. The efficacy and precision of the proposed methodology are demonstrated through a numerical example, applied in the context of an ICS security supplier. This example serves as a testament to the superiority of the approach in handling complex decision-making scenarios inherent in ICS-security management. ]]> Enhanced Industrial Control System of Decision-Making Using Spherical Hesitant Fuzzy Soft Yager Aggregation Information razia choudhary shabana ashraf jafar anafi doi: 10.56578/atams010304 Acadlore Transactions on Applied Mathematics and Statistics 12-12-2023 Acadlore Transactions on Applied Mathematics and Statistics 12-12-2023 2023 1 3 Article 161 10.56578/atams010304 https://www.acadlore.com/article/ATAMS/2023_1_3/atams010304 https://www.acadlore.com/article/ATAMS/2023_1_3/atams010303 In contemporary military contexts, the determination of an optimal course of action (COA) in combat operations emerges as a critical challenge. This study delineates a decision support methodology for military applications, employing sophisticated decision analysis techniques. The initial phase entails the identification of pivotal criteria for assessing and ranking COAs, followed by the assignment of weight coefficients to each criterion via the full consistency method (FUCOM). Subsequently, the Einstein weighted arithmetic average operator (EWAA) was utilized for the aggregation of expert opinions, ensuring a consensual evaluation of these criteria and culminating in the final values of their weight coefficients. The ensuing phase focuses on the selection of an optimal COA, incorporating the grey complex proportional assessment (COPRAS-G) method. This method addresses uncertainties and varying criterion values. Expert ratings were again aggregated using the EWAA operator. The findings from this phase are designed to provide military commanders with precise, data-driven guidance for decision-making. To validate and verify the stability of the proposed model, a series of tests were conducted, including a rank reversal test, sensitivity analysis regarding changes in weight coefficients, and a comparative analysis with alternative methods. These assessments uniformly indicated the model's consistency, stability, and validity as a military decision support tool. Emphasizing a high degree of confidence in COA selection, the methodology advocated herein is applicable to decision-making processes in the planning and execution of military operations. The uniform application of professional terms, consistent with the broader context of this research, ensures clarity and coherence in its presentation. The approach outlined in this study stands as a testament to rigorous analytical methodologies in the realm of military strategic planning, offering a robust framework for decision-making under conditions of uncertainty and complexity. 11-29-2023 <![CDATA[ In contemporary military contexts, the determination of an optimal course of action (COA) in combat operations emerges as a critical challenge. This study delineates a decision support methodology for military applications, employing sophisticated decision analysis techniques. The initial phase entails the identification of pivotal criteria for assessing and ranking COAs, followed by the assignment of weight coefficients to each criterion via the full consistency method (FUCOM). Subsequently, the Einstein weighted arithmetic average operator (EWAA) was utilized for the aggregation of expert opinions, ensuring a consensual evaluation of these criteria and culminating in the final values of their weight coefficients. The ensuing phase focuses on the selection of an optimal COA, incorporating the grey complex proportional assessment (COPRAS-G) method. This method addresses uncertainties and varying criterion values. Expert ratings were again aggregated using the EWAA operator. The findings from this phase are designed to provide military commanders with precise, data-driven guidance for decision-making. To validate and verify the stability of the proposed model, a series of tests were conducted, including a rank reversal test, sensitivity analysis regarding changes in weight coefficients, and a comparative analysis with alternative methods. These assessments uniformly indicated the model's consistency, stability, and validity as a military decision support tool. Emphasizing a high degree of confidence in COA selection, the methodology advocated herein is applicable to decision-making processes in the planning and execution of military operations. The uniform application of professional terms, consistent with the broader context of this research, ensures clarity and coherence in its presentation. The approach outlined in this study stands as a testament to rigorous analytical methodologies in the realm of military strategic planning, offering a robust framework for decision-making under conditions of uncertainty and complexity. ]]> Optimizing Military Decision-Making: Application of the FUCOM– EWAA–COPRAS-G MCDM Model duško tešić darko božanić doi: 10.56578/atams010303 Acadlore Transactions on Applied Mathematics and Statistics 11-29-2023 Acadlore Transactions on Applied Mathematics and Statistics 11-29-2023 2023 1 3 Article 148 10.56578/atams010303 https://www.acadlore.com/article/ATAMS/2023_1_3/atams010303 https://www.acadlore.com/article/ATAMS/2023_1_3/atams010302 In the realm of financial markets, the manifestation of volatility clustering serves as a pivotal element, indicative of the inherent fluctuations characterizing financial instruments. This attribute acquires pronounced relevance within the sphere of cryptocurrencies, a sector renowned for its elevated risk profile. The present analysis, conducted through the Autoregressive Moving Average - Generalized Autoregressive Conditional Heteroskedasticity (ARMA-GARCH) model, seeks to elucidate the enduring nature of volatility clustering and the occurrence of leverage effects within this domain. Over the course of a four-year time frame, it was observed that Bitcoin diverges from the anticipated Autoregressive Conditional Heteroskedasticity (ARCH) effects, in contrast to Ethereum and Cardano, which exhibit marked volatility clustering. Binance Coin, Ripple, and Dogecoin, whilst demonstrating moderate clustering, uniformly reflect the existence of leverage effects. An exception to this pattern was identified in Ripple, where it was discerned that positive market news exerts a disproportionate influence on log returns. The findings of this study illuminate the critical influence of both leverage effects and volatility clustering on the pricing dynamics of cryptocurrencies. It underscores the imperative for a nuanced comprehension of risk management in the context of cryptocurrency investments, given their susceptibility to abrupt price fluctuations. The distinct degrees to which these phenomena are manifested across diverse cryptocurrencies accentuate the necessity for a tailored risk management approach, resonant with the unique attributes of the asset in question. Such strategies, accounting for the potential amplification of losses through leverage, may encompass prudent position sizing, portfolio diversification, and the implementation of stress tests, thereby fortifying the investment against the dual perils of volatility clustering and leverage effects. The implications of this analysis serve to inform investors, providing a foundation upon which to construct risk management tactics that are responsive to the idiosyncrasies of the cryptocurrency market. 11-27-2023 <![CDATA[ In the realm of financial markets, the manifestation of volatility clustering serves as a pivotal element, indicative of the inherent fluctuations characterizing financial instruments. This attribute acquires pronounced relevance within the sphere of cryptocurrencies, a sector renowned for its elevated risk profile. The present analysis, conducted through the Autoregressive Moving Average - Generalized Autoregressive Conditional Heteroskedasticity (ARMA-GARCH) model, seeks to elucidate the enduring nature of volatility clustering and the occurrence of leverage effects within this domain. Over the course of a four-year time frame, it was observed that Bitcoin diverges from the anticipated Autoregressive Conditional Heteroskedasticity (ARCH) effects, in contrast to Ethereum and Cardano, which exhibit marked volatility clustering. Binance Coin, Ripple, and Dogecoin, whilst demonstrating moderate clustering, uniformly reflect the existence of leverage effects. An exception to this pattern was identified in Ripple, where it was discerned that positive market news exerts a disproportionate influence on log returns. The findings of this study illuminate the critical influence of both leverage effects and volatility clustering on the pricing dynamics of cryptocurrencies. It underscores the imperative for a nuanced comprehension of risk management in the context of cryptocurrency investments, given their susceptibility to abrupt price fluctuations. The distinct degrees to which these phenomena are manifested across diverse cryptocurrencies accentuate the necessity for a tailored risk management approach, resonant with the unique attributes of the asset in question. Such strategies, accounting for the potential amplification of losses through leverage, may encompass prudent position sizing, portfolio diversification, and the implementation of stress tests, thereby fortifying the investment against the dual perils of volatility clustering and leverage effects. The implications of this analysis serve to inform investors, providing a foundation upon which to construct risk management tactics that are responsive to the idiosyncrasies of the cryptocurrency market. ]]> The Cryptocurrency Market Through the Scope of Volatility Clustering and Leverage Effects filip peovski violeta cvetkoska igor ivanovski doi: 10.56578/atams010302 Acadlore Transactions on Applied Mathematics and Statistics 11-27-2023 Acadlore Transactions on Applied Mathematics and Statistics 11-27-2023 2023 1 3 Article 130 10.56578/atams010302 https://www.acadlore.com/article/ATAMS/2023_1_3/atams010302 https://www.acadlore.com/article/ATAMS/2023_1_3/atams010301 In the present investigation, the phenomena of multi-scale volatility spillovers and dynamic hedging within the Chinese stock market are scrutinized, with particular emphasis on the implications of structural breaks. The decomposition of the returns from the CSI 300 and Hang sheng index’ spot and futures is achieved through the application of the Maximum Overlap Discrete Wavelet Transform (MODWT), categorizing the data into three distinct temporal scales: short-term, medium-term, and long-term. An enhancement upon the conventional VAR-BEKK-GARCH (Vector Autoregressive - Baba, Engle, Kraft, and Kroner - Generalized Autoregressive Conditional Heteroskedasticity) model is proposed, yielding the asymmetric VAR-BEKK-GARCH Model (VAR-BEKK-AGARCH), which adeptly integrates the structural break of return volatility. A comprehensive analysis is conducted to elucidate the interactions and spillovers between the CSI 300 and Hang Seng Index, as well as their respective spot and futures markets, across the various identified time scales. Concurrently, a dynamic hedging portfolio, comprised of index spot and futures, is meticulously constructed, with its performance rigorously evaluated under the influence of the different time scales. To ensure the robustness and validity of the findings, wavelet coherence and phase difference methodologies are employed as verification tools. The results unequivocally reveal a heterogeneity in the behavior of mean spillover, volatility spillover, and asymmetric spillovers between the spot and futures markets of the CSI 300 and Hang Seng Index across the diverse scales. The inclusion of a structural break in the dynamic hedge portfolio is demonstrated to confer a marked advantage over its counterpart that omits this critical factor. Particularly in the short and medium-term scenarios, the dynamically hedged portfolio, enriched by the consideration of the structural break, exhibits superior performance in comparison to the static hedge portfolio. Additionally, it is discerned that the CSI 300 Index and Hang Seng Index, along with their spot and futures components, predominantly manifest in synchrony, with no clear indication of a consistent leader-lag relationship. An intensification of correlation is observed in the long-term analysis, underscoring the utility of the spot and futures of the two indices as efficacious hedging tools. 11-22-2023 <![CDATA[ In the present investigation, the phenomena of multi-scale volatility spillovers and dynamic hedging within the Chinese stock market are scrutinized, with particular emphasis on the implications of structural breaks. The decomposition of the returns from the CSI 300 and Hang sheng index’ spot and futures is achieved through the application of the Maximum Overlap Discrete Wavelet Transform (MODWT), categorizing the data into three distinct temporal scales: short-term, medium-term, and long-term. An enhancement upon the conventional VAR-BEKK-GARCH (Vector Autoregressive - Baba, Engle, Kraft, and Kroner - Generalized Autoregressive Conditional Heteroskedasticity) model is proposed, yielding the asymmetric VAR-BEKK-GARCH Model (VAR-BEKK-AGARCH), which adeptly integrates the structural break of return volatility. A comprehensive analysis is conducted to elucidate the interactions and spillovers between the CSI 300 and Hang Seng Index, as well as their respective spot and futures markets, across the various identified time scales. Concurrently, a dynamic hedging portfolio, comprised of index spot and futures, is meticulously constructed, with its performance rigorously evaluated under the influence of the different time scales. To ensure the robustness and validity of the findings, wavelet coherence and phase difference methodologies are employed as verification tools. The results unequivocally reveal a heterogeneity in the behavior of mean spillover, volatility spillover, and asymmetric spillovers between the spot and futures markets of the CSI 300 and Hang Seng Index across the diverse scales. The inclusion of a structural break in the dynamic hedge portfolio is demonstrated to confer a marked advantage over its counterpart that omits this critical factor. Particularly in the short and medium-term scenarios, the dynamically hedged portfolio, enriched by the consideration of the structural break, exhibits superior performance in comparison to the static hedge portfolio. Additionally, it is discerned that the CSI 300 Index and Hang Seng Index, along with their spot and futures components, predominantly manifest in synchrony, with no clear indication of a consistent leader-lag relationship. An intensification of correlation is observed in the long-term analysis, underscoring the utility of the spot and futures of the two indices as efficacious hedging tools. ]]> Risk Spillovers and Hedging in the Chinese Stock Market: An Asymmetric VAR-BEKK-AGARCH Analysis jia wang xun huang xu wang doi: 10.56578/atams010301 Acadlore Transactions on Applied Mathematics and Statistics 11-22-2023 Acadlore Transactions on Applied Mathematics and Statistics 11-22-2023 2023 1 3 Article 111 10.56578/atams010301 https://www.acadlore.com/article/ATAMS/2023_1_3/atams010301 https://www.acadlore.com/article/ATAMS/2023_1_2/atams010205 This paper presents an investigation of traveling wave solutions and a sensitivity analysis for the unidirectional Dullin-Gottwald-Holm ($DGH$) system, a well-established model for wave propagation in shallow water. We apply the novel auxiliary equation method, a unique integration norm, to extract various soliton solutions, including kink, rational, bright, singular, and bright-singular solutions. Precise explicit solutions of the resultant ordinary differential equations are demonstrated using suitable parametric values. Furthermore, we explore the conditions that ensure the existence of these solutions. By applying the Galilean transformation, we convert the model into a planar dynamical system and evaluate its sensitivity performance. The selection of appropriate parameters enables the generation of two and three-dimensional sketches, as well as contour plots for each solution. 09-29-2023 <![CDATA[ This paper presents an investigation of traveling wave solutions and a sensitivity analysis for the unidirectional Dullin-Gottwald-Holm ($DGH$) system, a well-established model for wave propagation in shallow water. We apply the novel auxiliary equation method, a unique integration norm, to extract various soliton solutions, including kink, rational, bright, singular, and bright-singular solutions. Precise explicit solutions of the resultant ordinary differential equations are demonstrated using suitable parametric values. Furthermore, we explore the conditions that ensure the existence of these solutions. By applying the Galilean transformation, we convert the model into a planar dynamical system and evaluate its sensitivity performance. The selection of appropriate parameters enables the generation of two and three-dimensional sketches, as well as contour plots for each solution. ]]> Analyzing Sensitivity and Solitonic Behavior Using the Dullin-Gottwald-Holm Model in Shallow Water Waves shaheera haroon muhammad abuzar muhammad faisal khan doi: 10.56578/atams010205 Acadlore Transactions on Applied Mathematics and Statistics 09-29-2023 Acadlore Transactions on Applied Mathematics and Statistics 09-29-2023 2023 1 2 Article 96 10.56578/atams010205 https://www.acadlore.com/article/ATAMS/2023_1_2/atams010205 https://www.acadlore.com/article/ATAMS/2023_1_2/atams010204 In businesses entailing the distribution of goods, the vehicle routing problem (VRP) critically influences the minimization of distribution costs and the curtailment of excessive vehicle utilization. This study delves into the formulation of the VRP within a firm specializing in the distribution of appliances and consumer goods, emphasizing the firm's unique operational characteristics. A mathematical model addressing the vehicle routing issue is meticulously crafted and subsequently resolved, yielding exact solutions through the application of the GNU Linear Programming Kit (GLPK). Comparative insights into the pre-existing and newly devised routing methodologies within the firm are elucidated. Owing to the dynamism in customer demands and daily deliveries, the propounded model has been designed for facile adaptability and frequent utilization. It demonstrates a marked enhancement over the conventional routing paradigms prevalent within the company. Recognizing potential avenues for advancement, considerations such as multi-warehouse integration and the introduction of customer-specific time windows, wherein goods must be dispatched within stipulated intervals, are acknowledged as prospects for future research and implementation. 09-21-2023 <![CDATA[ In businesses entailing the distribution of goods, the vehicle routing problem (VRP) critically influences the minimization of distribution costs and the curtailment of excessive vehicle utilization. This study delves into the formulation of the VRP within a firm specializing in the distribution of appliances and consumer goods, emphasizing the firm's unique operational characteristics. A mathematical model addressing the vehicle routing issue is meticulously crafted and subsequently resolved, yielding exact solutions through the application of the GNU Linear Programming Kit (GLPK). Comparative insights into the pre-existing and newly devised routing methodologies within the firm are elucidated. Owing to the dynamism in customer demands and daily deliveries, the propounded model has been designed for facile adaptability and frequent utilization. It demonstrates a marked enhancement over the conventional routing paradigms prevalent within the company. Recognizing potential avenues for advancement, considerations such as multi-warehouse integration and the introduction of customer-specific time windows, wherein goods must be dispatched within stipulated intervals, are acknowledged as prospects for future research and implementation. ]]> Optimal Vehicle Routing in Consumer Goods Distribution: A GNU Linear Programming Kit-Based Analysis uroš dedović bisera andrić gušavac doi: 10.56578/atams010204 Acadlore Transactions on Applied Mathematics and Statistics 09-21-2023 Acadlore Transactions on Applied Mathematics and Statistics 09-21-2023 2023 1 2 Article 87 10.56578/atams010204 https://www.acadlore.com/article/ATAMS/2023_1_2/atams010204 https://www.acadlore.com/article/ATAMS/2023_1_2/atams010203 In recent years, a surge in studies concerning indigenous knowledge (IK) has been observed, yet a clear definition of IK remains elusive. Discrepancies in international studies lead to fluid interpretations of the concept. The present study seeks to delineate the key elements characterizing knowledge as either indigenous or foreign to a specific community. Through a meticulous exploration of definitions surrounding indigenous knowledge, it is posited that all knowledge forms can be considered indigenous within the communities of their origination. To elucidate this argument, the impact of community demographics on the adoption of knowledge perceived as indigenous within the Chief Albert Luthuli Municipality was investigated. Data were collected using structured interviews, involving a total of 398 respondents. Analyses were conducted employing a mixed-method approach, utilizing Microsoft Excel and the Statistical Package for Social Sciences (SPSS). Findings revealed a significant relationship between variables such as commonly spoken language, cultural attributes, age, and employment level with IK practices within communities. Furthermore, the economic factors, including employment status, education levels, and household income, were examined for their association with the adoption of IK practices. It was discerned that such variables were correlated with the adoption of IK practices, especially as alternative strategies in the absence of consistent household income. Key determinants like the language proficiency of the household head, employment status, educational attainment, family size, household income level, age, and gender of the household heads were analyzed. The influence of these determinants on household adoption of indigenous practices was assessed using inferential statistical methods, specifically probability and regression analysis. 09-21-2023 <![CDATA[ <p>In recent years, a surge in studies concerning indigenous knowledge (IK) has been observed, yet a clear definition of IK remains elusive. Discrepancies in international studies lead to fluid interpretations of the concept. The present study seeks to delineate the key elements characterizing knowledge as either indigenous or foreign to a specific community. Through a meticulous exploration of definitions surrounding indigenous knowledge, it is posited that all knowledge forms can be considered indigenous within the communities of their origination. To elucidate this argument, the impact of community demographics on the adoption of knowledge perceived as indigenous within the Chief Albert Luthuli Municipality was investigated. Data were collected using structured interviews, involving a total of 398 respondents. Analyses were conducted employing a mixed-method approach, utilizing Microsoft Excel and the Statistical Package for Social Sciences (SPSS). Findings revealed a significant relationship between variables such as commonly spoken language, cultural attributes, age, and employment level with IK practices within communities. Furthermore, the economic factors, including employment status, education levels, and household income, were examined for their association with the adoption of IK practices. It was discerned that such variables were correlated with the adoption of IK practices, especially as alternative strategies in the absence of consistent household income. Key determinants like the language proficiency of the household head, employment status, educational attainment, family size, household income level, age, and gender of the household heads were analyzed. The influence of these determinants on household adoption of indigenous practices was assessed using inferential statistical methods, specifically probability and regression analysis.</p> ]]> Demographic Influences on Indigenous Knowledge Practices in Chief Albert Luthuli Municipality matlhodi famo machate machate doi: 10.56578/atams010203 Acadlore Transactions on Applied Mathematics and Statistics 09-21-2023 Acadlore Transactions on Applied Mathematics and Statistics 09-21-2023 2023 1 2 Article 77 10.56578/atams010203 https://www.acadlore.com/article/ATAMS/2023_1_2/atams010203 https://www.acadlore.com/article/ATAMS/2023_1_2/atams010202 The process of decision-making involves selecting the most suitable management action from a range of options, thereby guiding the system towards its management objectives. Within the complex decision-making environment, uncertainty prevails, giving rise to the domain of risk. Effective risk management entails various activities that are implemented during distinct phases of system management. To address this, a systemic approach to risk management is crucial, along with the adoption of software solutions for risk analysis. This study examines the systemic approach to risk management and proposes a potential solution for managing uncertainties and risks by employing software tools that are rooted in system quality. System quality encompasses the development of novel models, methods, tools, and procedures, whose consistent application ensures reliable outcomes based on the best available information. Consequently, this study explores the application of innovative software solutions that support the risk management process across all phases. Given that risk management relies on data, which may not offer a comprehensive view of the environment, decision-making can be regarded as a process of managing the conversion of data into information. The acquisition of new information regarding the system's state determines the approach to modify the system through the chosen decision. Information serves as the essence of the decision-making process, as quality information facilitates quality decisions. However, in an information space characterized by incomplete data, the quality of decisions diminishes. Software solutions capable of providing the necessary level of information quality, despite uncertainties and incompleteness, enable decision-making based on partial information while upholding a minimum standard of quality. 08-20-2023 <![CDATA[ <p>The process of decision-making involves selecting the most suitable management action from a range of options, thereby guiding the system towards its management objectives. Within the complex decision-making environment, uncertainty prevails, giving rise to the domain of risk. Effective risk management entails various activities that are implemented during distinct phases of system management. To address this, a systemic approach to risk management is crucial, along with the adoption of software solutions for risk analysis. This study examines the systemic approach to risk management and proposes a potential solution for managing uncertainties and risks by employing software tools that are rooted in system quality. System quality encompasses the development of novel models, methods, tools, and procedures, whose consistent application ensures reliable outcomes based on the best available information. Consequently, this study explores the application of innovative software solutions that support the risk management process across all phases. Given that risk management relies on data, which may not offer a comprehensive view of the environment, decision-making can be regarded as a process of managing the conversion of data into information. The acquisition of new information regarding the system's state determines the approach to modify the system through the chosen decision. Information serves as the essence of the decision-making process, as quality information facilitates quality decisions. However, in an information space characterized by incomplete data, the quality of decisions diminishes. Software solutions capable of providing the necessary level of information quality, despite uncertainties and incompleteness, enable decision-making based on partial information while upholding a minimum standard of quality.</p> ]]> A Systemic Approach to Risk Management: Utilizing Decision Support Software Solutions for Enhanced Decision-Making nenad komazec katarina jankovic doi: 10.56578/atams010202 Acadlore Transactions on Applied Mathematics and Statistics 08-20-2023 Acadlore Transactions on Applied Mathematics and Statistics 08-20-2023 2023 1 2 Article 66 10.56578/atams010202 https://www.acadlore.com/article/ATAMS/2023_1_2/atams010202 https://www.acadlore.com/article/ATAMS/2023_1_2/atams010201 Goodwill impairment, resulting from the impairment tests conducted on goodwill generated during business mergers, serves as an effective indicator of a company's true and reliable goodwill value, as well as its operational and financial conditions. This study investigates the impact of earnings management motivations on goodwill impairment from the perspective of corporate governance, focusing on Chinese manufacturing listed companies between 2016 and 2020. Utilizing regression analysis and panel data models, the study examines the internal governance mechanisms, including the combined shareholding ratio of the top ten shareholders, and the external governance mechanisms, such as the role of the four major auditing firms. The findings reveal that both "big bath" and earnings smoothing motives can influence companies' decisions to recognize goodwill impairment, while effective internal and external governance mechanisms can help mitigate earnings management motivations. Further analysis shows that non-state-owned manufacturing listed companies are more likely to exhibit goodwill impairment behaviors driven by earnings management motives. These findings provide valuable insights for listed companies seeking to improve their corporate governance structures and for Chinese capital market regulators aiming to enhance relevant regulatory policies and refine goodwill measurement standards. 06-18-2023 <![CDATA[ <p>Goodwill impairment, resulting from the impairment tests conducted on goodwill generated during business mergers, serves as an effective indicator of a company's true and reliable goodwill value, as well as its operational and financial conditions. This study investigates the impact of earnings management motivations on goodwill impairment from the perspective of corporate governance, focusing on Chinese manufacturing listed companies between 2016 and 2020. Utilizing regression analysis and panel data models, the study examines the internal governance mechanisms, including the combined shareholding ratio of the top ten shareholders, and the external governance mechanisms, such as the role of the four major auditing firms. The findings reveal that both "big bath" and earnings smoothing motives can influence companies' decisions to recognize goodwill impairment, while effective internal and external governance mechanisms can help mitigate earnings management motivations. Further analysis shows that non-state-owned manufacturing listed companies are more likely to exhibit goodwill impairment behaviors driven by earnings management motives. These findings provide valuable insights for listed companies seeking to improve their corporate governance structures and for Chinese capital market regulators aiming to enhance relevant regulatory policies and refine goodwill measurement standards.</p> ]]> An Empirical Analysis of Corporate Governance and Earnings Management Motives Influencing Goodwill Impairment in Chinese Manufacturing Firms cheng wang ting hu doi: 10.56578/atams010201 Acadlore Transactions on Applied Mathematics and Statistics 06-18-2023 Acadlore Transactions on Applied Mathematics and Statistics 06-18-2023 2023 1 2 Article 51 10.56578/atams010201 https://www.acadlore.com/article/ATAMS/2023_1_2/atams010201 https://www.acadlore.com/article/ATAMS/2023_1_1/atams010105 Existing legal and by-law regulations prescribe risk management methodologies for various domains, such as the transportation of hazardous materials, fire and explosion protection, environmental protection, and protection against chemical accidents. However, there is a lack of comprehensive methodological guidance that unifies the management of all risks associated with the transportation of explosive remnants of war (ERW), which pose significant threats to human life, cultural assets, and the environment. Furthermore, the transportation of ERW often occurs along traffic corridors with compromised infrastructure, increasing the range of potential risks affecting the safety of people, their property, and critical infrastructure. This study presents an integrated risk management model for ERW transportation in the Republic of Serbia, developed based on current legal and by-law regulations, as well as modern criteria and risk assessment methodologies. By applying this model, the various risks associated with ERW transportation can be effectively mitigated, ensuring the safety and protection of people, assets, and the environment. 06-13-2023 <![CDATA[ <p>Existing legal and by-law regulations prescribe risk management methodologies for various domains, such as the transportation of hazardous materials, fire and explosion protection, environmental protection, and protection against chemical accidents. However, there is a lack of comprehensive methodological guidance that unifies the management of all risks associated with the transportation of explosive remnants of war (ERW), which pose significant threats to human life, cultural assets, and the environment. Furthermore, the transportation of ERW often occurs along traffic corridors with compromised infrastructure, increasing the range of potential risks affecting the safety of people, their property, and critical infrastructure. This study presents an integrated risk management model for ERW transportation in the Republic of Serbia, developed based on current legal and by-law regulations, as well as modern criteria and risk assessment methodologies. By applying this model, the various risks associated with ERW transportation can be effectively mitigated, ensuring the safety and protection of people, assets, and the environment.</p> ]]> An Integrated Risk Management Model for Transporting Explosive Remnants of War: A Case Study in the Republic of Serbia nenad komazec katarina jankovic doi: 10.56578/atams010105 Acadlore Transactions on Applied Mathematics and Statistics 06-13-2023 Acadlore Transactions on Applied Mathematics and Statistics 06-13-2023 2023 1 1 Article 44 10.56578/atams010105 https://www.acadlore.com/article/ATAMS/2023_1_1/atams010105 https://www.acadlore.com/article/ATAMS/2023_1_1/atams010104 The advent of air travel, originally proposed by the Wright brothers, has led to a significant surge in aircraft usage for human transportation. In its nascent stages, this mode of transport was linked with a high frequency of accidents and consequent fatalities, placing it in the high-risk category. To counter these risks, the International Civil Aviation Organization (ICAO) was established in 1947 as a collaborative effort among numerous countries with the primary goal of enhancing aviation safety regulations. This study analyzed archival data from the Bureau of Aircraft Accidents Archives (B3A), covering a span of 72 years from 1918, the year of the first commercial airplane crash, until 2020. The objective was to understand the ICAO's impact on altering accident rates, fatalities, and underlying causes. Analytical methodologies encompassed both descriptive statistics—examining data distribution, central tendencies, and category frequencies—and exploratory data analysis (EDA) to identify variable relationships and outlier identification. The results indicated that ICAO's interventions have led to a notable decline in accident rates, with an annual average reduction of 70.9%, and a corresponding decrease in incidents attributed to technical factors. However, an unexpected trend was the increase in fatalities despite the drop in accident numbers, attributable to the introduction of larger aircraft designs carrying more passengers per flight. The findings underscore the ICAO's successful efforts in reducing aircraft accidents, but also suggest a need for further exploration into factors contributing to the rise in fatalities. 06-13-2023 <![CDATA[ <p>The advent of air travel, originally proposed by the Wright brothers, has led to a significant surge in aircraft usage for human transportation. In its nascent stages, this mode of transport was linked with a high frequency of accidents and consequent fatalities, placing it in the high-risk category. To counter these risks, the International Civil Aviation Organization (ICAO) was established in 1947 as a collaborative effort among numerous countries with the primary goal of enhancing aviation safety regulations. This study analyzed archival data from the Bureau of Aircraft Accidents Archives (B3A), covering a span of 72 years from 1918, the year of the first commercial airplane crash, until 2020. The objective was to understand the ICAO's impact on altering accident rates, fatalities, and underlying causes. Analytical methodologies encompassed both descriptive statistics—examining data distribution, central tendencies, and category frequencies—and exploratory data analysis (EDA) to identify variable relationships and outlier identification. The results indicated that ICAO's interventions have led to a notable decline in accident rates, with an annual average reduction of 70.9%, and a corresponding decrease in incidents attributed to technical factors. However, an unexpected trend was the increase in fatalities despite the drop in accident numbers, attributable to the introduction of larger aircraft designs carrying more passengers per flight. The findings underscore the ICAO's successful efforts in reducing aircraft accidents, but also suggest a need for further exploration into factors contributing to the rise in fatalities.</p> ]]> Evaluating the Influence of the International Civil Aviation Organization on Aircraft Accident Rates and Fatalities: A Seven-Decade Historical Data Analysis rossi passarella harumi veny muhammad fachrurrozi samsuryadi samsuryadi marsella vindriani doi: 10.56578/atams010104 Acadlore Transactions on Applied Mathematics and Statistics 06-13-2023 Acadlore Transactions on Applied Mathematics and Statistics 06-13-2023 2023 1 1 Article 33 10.56578/atams010104 https://www.acadlore.com/article/ATAMS/2023_1_1/atams010104 https://www.acadlore.com/article/ATAMS/2023_1_1/atams010103 The continuous evolution of consumer behavior in the modern era of consumption has prompted enterprises to explore the underlying behavioral factors of consumers and cater to their particular needs. Moreover, developing a rational operational behavior model and responding effectively to the dynamic market environment have become critical concerns for businesses. This study examines the impact of consumer reference price effects and enterprise short-sighted behavior on strategic selection and performance, employing differential game theory to construct a game model between manufacturers and retailers. Utilizing Behrman's continuous dynamic programming theory, analytical solutions for various models are derived, followed by comparative analyses and numerical examples. The research reveals that: (1) manufacturers' behavior patterns are found to be dominant, favoring far-sighted behavior, which not only enhances profits but also enables consumers to access higher quality and cost-effective products; retailers should opt for collaboration with far-sighted manufacturers and exhibit a preference for short-sighted behavior. (2) In terms of overall system profit, the FM model emerges as the optimal combination. (3) When the reference price effect has a small impact on market demand, enterprises can make use of the reference price effect to actively promote marketing and gain profit; as the influence increases, intensifying the degree of influence effectively augments profits. 06-07-2023 <![CDATA[ <p>The continuous evolution of consumer behavior in the modern era of consumption has prompted enterprises to explore the underlying behavioral factors of consumers and cater to their particular needs. Moreover, developing a rational operational behavior model and responding effectively to the dynamic market environment have become critical concerns for businesses. This study examines the impact of consumer reference price effects and enterprise short-sighted behavior on strategic selection and performance, employing differential game theory to construct a game model between manufacturers and retailers. Utilizing Behrman's continuous dynamic programming theory, analytical solutions for various models are derived, followed by comparative analyses and numerical examples. The research reveals that: (1) manufacturers' behavior patterns are found to be dominant, favoring far-sighted behavior, which not only enhances profits but also enables consumers to access higher quality and cost-effective products; retailers should opt for collaboration with far-sighted manufacturers and exhibit a preference for short-sighted behavior. (2) In terms of overall system profit, the FM model emerges as the optimal combination. (3) When the reference price effect has a small impact on market demand, enterprises can make use of the reference price effect to actively promote marketing and gain profit; as the influence increases, intensifying the degree of influence effectively augments profits.</p> ]]> Dynamic Operational Strategies Incorporating Consumer Reference Price Effects and Enterprise Behavior: A Differential Game Approach fangfang guo zhuang wu yuanyuan wang jiaqi du wanshu fu doi: 10.56578/atams010103 Acadlore Transactions on Applied Mathematics and Statistics 06-07-2023 Acadlore Transactions on Applied Mathematics and Statistics 06-07-2023 2023 1 1 Article 22 10.56578/atams010103 https://www.acadlore.com/article/ATAMS/2023_1_1/atams010103 https://www.acadlore.com/article/ATAMS/2023_1_1/atams010102 This study aims to identify efficient Information Technology (IT) candidates for a specific position and highlight areas for improvement using Data Envelopment Analysis (DEA). By streamlining the selection process and reducing costs, the findings can assist companies in making better-informed hiring decisions. Additionally, the results provide candidates with valuable feedback on areas for development, increasing their chances of securing employment in their desired company. The DEA model offers a unique advantage in this context by generating reference units for each candidate, enabling precise determination of the necessary changes in inputs or outputs for achieving efficiency. The Charnes, Cooper, and Rhodes (CCR) model served as the baseline, with parallel comparisons drawn against the Banker, Charnes, and Cooper (BCC) and categorical models to identify the most effective approach. The findings reveal the efficient candidates based on the assessed criteria, demonstrating that less experienced candidates can be evaluated as efficient compared to their more experienced counterparts. The hypothesis that the BCC model, with its more flexible efficiency frontier, results in poorer candidate differentiation was confirmed. This study highlights the value of adopting the DEA method in evaluating the employment efficiency of IT candidates, offering practical implications for both hiring organizations and job-seekers. 06-06-2023 <![CDATA[ <p>This study aims to identify efficient Information Technology (IT) candidates for a specific position and highlight areas for improvement using Data Envelopment Analysis (DEA). By streamlining the selection process and reducing costs, the findings can assist companies in making better-informed hiring decisions. Additionally, the results provide candidates with valuable feedback on areas for development, increasing their chances of securing employment in their desired company. The DEA model offers a unique advantage in this context by generating reference units for each candidate, enabling precise determination of the necessary changes in inputs or outputs for achieving efficiency. The Charnes, Cooper, and Rhodes (CCR) model served as the baseline, with parallel comparisons drawn against the Banker, Charnes, and Cooper (BCC) and categorical models to identify the most effective approach. The findings reveal the efficient candidates based on the assessed criteria, demonstrating that less experienced candidates can be evaluated as efficient compared to their more experienced counterparts. The hypothesis that the BCC model, with its more flexible efficiency frontier, results in poorer candidate differentiation was confirmed. This study highlights the value of adopting the DEA method in evaluating the employment efficiency of IT candidates, offering practical implications for both hiring organizations and job-seekers.</p> ]]> Evaluating the Employment Efficiency of IT Candidates Using Data Envelopment Analysis andjela mrdak tijana nanuševski doi: 10.56578/atams010102 Acadlore Transactions on Applied Mathematics and Statistics 06-06-2023 Acadlore Transactions on Applied Mathematics and Statistics 06-06-2023 2023 1 1 Article 10 10.56578/atams010102 https://www.acadlore.com/article/ATAMS/2023_1_1/atams010102 https://www.acadlore.com/article/ATAMS/2023_1_1/atams010101 Historically, infectious diseases have greatly impacted human health, necessitating a robust understanding of their trends, processes, and transmission. This study focuses on the COVID-19 pandemic, employing mathematical, statistical, and machine-learning methods to examine its time-series data. We quantify data irregularity using approximate entropy, revealing higher volatility in the U.S., Italy, and India compared to China. We employ the Dynamic Time Warping algorithm to assess regional similarity, finding a strong correlation between the U.S. and Italy. The Seasonal Trend Decomposition using the LOESS algorithm illuminates strong trend degrees in all observed regions, but China's prevention measures show marked effectiveness. These tools, whilst already valuable, still present opportunities for development in both theory and practice. 06-04-2023 <![CDATA[ <p>Historically, infectious diseases have greatly impacted human health, necessitating a robust understanding of their trends, processes, and transmission. This study focuses on the COVID-19 pandemic, employing mathematical, statistical, and machine-learning methods to examine its time-series data. We quantify data irregularity using approximate entropy, revealing higher volatility in the U.S., Italy, and India compared to China. We employ the Dynamic Time Warping algorithm to assess regional similarity, finding a strong correlation between the U.S. and Italy. The Seasonal Trend Decomposition using the LOESS algorithm illuminates strong trend degrees in all observed regions, but China's prevention measures show marked effectiveness. These tools, whilst already valuable, still present opportunities for development in both theory and practice.</p> ]]> Temporal Analysis of Infectious Diseases: A Case Study on COVID-19 jinyang liu boping tian jiaxuan wu doi: 10.56578/atams010101 Acadlore Transactions on Applied Mathematics and Statistics 06-04-2023 Acadlore Transactions on Applied Mathematics and Statistics 06-04-2023 2023 1 1 Article 1 10.56578/atams010101 https://www.acadlore.com/article/ATAMS/2023_1_1/atams010101