Water distribution networks are susceptible to abrupt pressure fluctuations and spikes due to rapid adjustments in valve and pump settings. A common occurrence resulting from the sudden closure of a valve, known as water hammer, can potentially cause damage to various components within the network if not adequately addressed. Traditionally, water hammer phenomena have been modeled using a set of hyperbolic partial differential equations (PDEs). This study introduces a simplified model that employs switched differential-algebraic equations (DAEs). Recognized for their capacity to generate infinite peaks in response to sudden structural changes, switched DAEs provide mathematical representations of infinite peaks, manifested as Dirac impulses. This modeling approach offers the potential for more straightforward analyses of complex water networks in future research. To validate the proposed technique, a numerical comparison was conducted between the PDE- and DAE-based models, using a basic configuration consisting of two reservoirs, a pipe, and a valve.

Developed countries have successfully implemented various Industry 4.0 (I4.0) initiatives, showcasing their ability to reap the benefits of this new industrial revolution. Active pursuit of excellence in Industry 4.0 is evident in these nations. However, in Africa, many countries still lack a clear understanding of Industry 4.0, with some remaining trapped in Industry 1.0 and others facing challenges in transitioning to Industry 2.0. Moreover, a significant number of these African countries continue to grapple with limited access to reliable electricity. To address the issue, this study examines seven strategies identified as criteria for enhancing the adoption of Industry 4.0 within the East African Community (EAC). These strategies are derived from observations of Industry 4.0 initiatives implemented in developed countries. Subsequently, the criteria are used to evaluate and rank the level of Industry 4.0 adoption in two specific East African countries. To tackle the challenges of complex group decision-making, the study integrates the Weighted Aggregated Sum Product Assessment (WASPAS) technique with the Step-Wise Weight Assessment Ratio Analysis (SWARA) within a spherical fuzzy (SF) framework. The SF-SWARA approach is applied to determine the weight and importance of the criteria, while SF-WASPAS is employed to rank the countries based on the criteria weighted by SF-SWARA. According to the findings, it was revealed that education and training, research, development, and innovation, as well as public-private partnerships and policy innovation, are the three most influential strategies for significantly improving the adoption of Industry 4.0 within the East African community. Furthermore, the results indicate that Rwanda stands out as the leading country in terms of implementing these strategies to enhance the adoption of Industry 4.0 technology. To verify the reliability and suitability of the proposed methodology, a sensitivity analysis was conducted, which affirmed the stability and practicality of the suggested approach.

Libya's strategic position at the crossroads of Europe and Africa offers access to abundant raw materials, labor, and extensive land for establishing free trade zones. The primary objective of this research is to determine the key advantages and opportunities that Libya could potentially leverage as a transit trade hub in the Mediterranean region through the establishment of free trade zones. This study investigates the extent to which Libya facilitates the expansion of commerce between Europe and Africa via initiatives related to free trade zones. Six criteria were employed in the present research, including economic, social, financial, environmental, quality, and demand factors. A panel of experts evaluated these criteria. The Full Consistency Method (FUCOM) was utilized to derive the criteria weights, with the economic criterion identified as the most significant. The Grey-CoCoSo (Combined Compromise Solution) methodology was applied to rank the industries eligible for investment within Libya's free zones. According to the findings, the food sector holds the highest importance in relation to investment.

This study presents an advanced generalization of uncertain linguistic numbers (ULNs) and interval-valued intuitionistic uncertain linguistic numbers (IVIULNs) through the development of interval-valued picture fuzzy numbers (IVPFNs). Firstly, the IVPFUL weighted average and IVPFUL weighted geometric operators, denoted as IVPFULWA and IVPFULWG, have been introduced. Furthermore, the IVPFUL Dombi weighted average and geometric operators, represented by IVPFULDWA and IVPFULDWG, are also proposed in the same context. These operators are utilized to establish a multi-attribute decision-making (MADM) approach with IVPFUL data. Finally, the proposed methodology is applied to a mutual fund selection problem through a demonstrative example.

This study focuses on formulating an integration algorithm for manufacturing firms aiming to infuse the immense potential of Industry 4.0 technologies into lean manufacturing systems. The goal is to unlock and harness the advantages offered by these advanced technologies in an economically efficient manner. An analytic approach has been implemented in this investigation, examining a broad array of relevant empirical research. This comprehensive analysis serves to derive a universal algorithm predicated on the principles of both lean methodology and Industry 4.0. The complexities and challenges of amalgamating lean methodology and Industry 4.0 have been scrutinized meticulously in this study. The study elaborates on the extent to which Industry 4.0 technologies can augment lean production practices, delves into the difficulties encountered by corporations during the integration process, and suggests measures to surmount these obstacles. Moreover, potential benefits realized through this integration are explored. The algorithm proffered in this study permits a phased integration approach. Firms have the flexibility to adopt the integration in specific production segments or processes initially and progressively expand, aligning with their capabilities, resources, and the level of process maturity. Such an integration strategy allows companies to leverage Industry 4.0 in overcoming restrictions traditionally associated with the lean approach.