For reducing uncertainty in data gathered from real-world scenarios, the picture fuzzy rough set (PFRS) framework is a reliable resource. This article presents new aggregation operators (AOs) based on the Schweizer-Sklar t-conorm (SS-TC) and Schweizer-Sklar t-norm (SS-TN). They present the PFRS framework with SS, which aims to handle the intricacies in contexts where decision-making is marked by ambiguity and uncertainty. In the context of Green Supply Chain Management (GSCM), where supply chain procedures incorporate sustainability considerations, this framework is especially pertinent. GSCM places a strong emphasis on minimizing environmental impacts by employing techniques such as effective resource management and sustainable sourcing. The adaptability and versatility required to assess and optimize these inexperienced practices are significantly improved with the aid of our expert PFRS framework. Businesses can keep operational efficiency and align their supply chain operations with environmental desires with the aid of using this framework. By considering both the blessings and disadvantages of environmental sustainability, using PFRS in GSCM enhances decision-making and promotes environmental sustainability. To handle picture fuzzy rough values (PFRVs), these operators include picture fuzzy rough weighted averaging (PFRSSWA) and picture fuzzy rough weighted geometric (PFRSSWG) operators. We investigate these recently created AOs' basic characteristics and use them to solve multi-attribute group decision-making (MAGDM) issues under the framework of picture fuzzy (PF) data. Our results demonstrate how the outcomes in SS-TN and SS-TC vary with varying parameter values. We also contrast these outcomes with the ones obtained from pre-existing AOs. In addition, we provide a graphic representation of all observations and findings to show how flexible and successful the suggested operators are at handling MAGDM problems.
Accurate selective image segmentation continues to pose substantial challenges, particularly under conditions of noise interference, intensity inhomogeneity, and irregular object boundaries. To address these complexities, a novel framework is introduced that integrates fuzzy Einstein–Dombi (ED) operators with level set energy minimization, guided by marker-based initialization. The proposed approach departs from traditional intensity-driven models by jointly incorporating intensity, texture, and gradient-based features, thereby facilitating improved boundary delineation and enhanced regional homogeneity. A spatially adaptive regularization term has been embedded within the level set formulation to reinforce contour stability and robustness in the presence of artefacts and signal degradation. The fuzzy ED operators enable nuanced fusion of multiple features through non-linear aggregation, yielding a more expressive and resilient energy functional. In contrast to conventional segmentation schemes, the developed method achieves superior convergence and delineation accuracy, particularly within complex grayscale and noisy medical image datasets. Experimental validation has been conducted across a range of imaging conditions, with performance quantitatively assessed using established metrics, including segmentation accuracy (0.95), intersection over union (IoU: 0.89), and Dice similarity coefficient (DSC: 0.94). These results demonstrate statistically significant improvements over comparative models. Additionally, qualitative evaluations reveal enhanced contour fidelity and resistance to local intensity fluctuations. The methodological simplicity and computational efficiency of the framework render it highly suitable for real-time applications in medical imaging diagnostics, object detection, and related image analysis tasks. By offering a robust, interpretable, and generalizable solution, this work establishes a new reference point for selective image segmentation under non-ideal conditions, and paves the way for further exploration of fuzzy operator integration within variational segmentation paradigms.
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