In the last few decades, there has been a significant increase in the importance of assessing social and ecological implications within industrial product supply chains. This tendency has given rise to the notion of supplier sustainability, which entails meeting the economic, environmental, and social demands of all suppliers. The supplier selections are typically based on experts’ opinion, which are then reflected in supplier ratings. When examining sustainability indicators, experts may not be fully aware of all aspects of suppliers’ economic, social, and environmental qualities. In the Decision Making (DM) approaches such as Pythagorean Fuzzy (PF) and q-Rung Orthopair Fuzzy (q-ROF) sets, experts are unable to use different powers for membership and non-membership grades simultaneously. In real-life DM problems, experts may require different power levels for membership and non-membership grades. In this paper, we propose a new extension of the COPRAS method under p, q-Quasirung orthopair fuzzy ( $p,q-$ QOF) sets, which allow decision-makers to use different power levels for membership and non-membership grades by incorporating parameters p and q. In the proposed approach, it is assumed that in addition to compiling the expert scores for suppliers, the issue analyst evaluates each expert’s degree of expertise for each criterion. The best choice is then determined by combining the data using the COPRAS method. The Inter-Criteria Correlation (CRITIC) method is employed to determine the unknown criteria weights. To demonstrate the effectiveness of our proposed approach, we apply it to a Multi-Criteria Group Decision-Making (MCGDM) problem that is focused on green supplier selection. Finally, we conduct a comparative study with existing approaches to demonstrate the practicality and applicability of the proposed DM method.

In the current era, IoT-based healthcare solutions play a pivotal role in transforming the healthcare landscape by addressing key challenges and significantly enhancing the quality, accessibility, and efficiency of medical services, particularly for individuals in remote areas. This paper introduces innovative operations on fractional fuzzy sets (FFS), specifically the Hamacher sum and product, and establishes corresponding operational laws. Building upon these foundations, we propose novel aggregation operators (AoPs) leveraging Hamacher norms and rigorously analyze their properties within the FFS framework. Furthermore, we integrate these advancements into decision-making methodologies, including Extended TOPSIS, TODIM, and Extended GRA, tailored for applications in FFS. To illustrate the practicality and effectiveness of our approach, we present a detailed case study on healthcare system selection. Finally, a comparative analysis of the proposed methods with existing aggregation operators highlights the robustness and suitability of our solution in real-world scenarios.

Despite advancements in divergence and distance measures across fuzzy set extensions, the development of such measures for Globular T-Spherical Fuzzy Sets (G-TSFSs) remains significantly unexplored. Existing approaches often fall short in capturing the rich semantics and high-dimensional uncertainty that G-TSFSs represent, limiting their utility in complex decision environments. This study is motivated by the need to fill this critical gap and advance decision science through more expressive and structurally aligned tools. This paper introduces a suite of novel divergence measures (Div-Ms) specifically formulated for G-TSFSs, a powerful tool for capturing uncertainty in multi-criteria group decision-making (MCGDM) under complex conditions. These Div-Ms serve as the foundation for developing new distance measures (Dis-Ms) and similarity measures (SMs), where both Dis-Ms and SMs are symmetry-based and their essential mathematical properties and supporting theorems are rigorously established. Leveraging these constructs, we propose a robust G-TSF-TOPSIS framework and apply it to a real-world problem, selecting optimal solar energy systems (SESs) for a university context. The model integrates expert evaluations, assuming equal importance due to their pivotal and complementary roles. A sensitivity analysis over the tunable parameter (ranging from 4.0 to 5.0 with an increment of 0.2) confirms the robustness and stability of the decision outcomes, with no changes observed in the final rankings. Comparative analysis with existing models shows superiority and soundness of the proposed methods. These results underscore the practical significance and theoretical soundness of the proposed approach. The study concludes by acknowledging its limitations and suggesting directions for future research, particularly in exploring adaptive expert weighting strategies for broader applicability.

Green supply chain management (GSCM) has become essential for organizations seeking to balance environmental sustainability, regulatory compliance, and economic resilience. However, selecting appropriate green supply chain strategies constitutes a complex multicriteria decision-making (MCDM) problem due to diverse sustainability practices, conflicting objectives, dynamic market conditions, and significant uncertainty in expert evaluations. To address these challenges, this study proposes an intelligent multicriteria group decision-making (MCGDM) framework to assess 15 GSCM strategies across 15 environmental, operational, economic, and regulatory criteria. The framework employs complex fractional orthopair fuzzy sets $\left(C_{FOFS}\right)$ to model uncertainty, expert hesitation, and complex-valued judgments. Expert weights are determined using the analytic hierarchy process (AHP), while criteria weights are derived objectively through the entropy method. A modified technique for order preference by similarity to the ideal solution (TOPSIS) is applied to obtain a robust ranking of alternatives. Evaluations from five multidisciplinary experts ensure practical relevance and validity. The results indicate enhanced uncertainty modeling, improved ranking stability, and greater interpretability compared with conventional fuzzy and deterministic approaches. The proposed framework provides a transparent and effective decision support tool for strategic GSCM planning.

Model selection in data science involves evaluating multiple alternatives across conflicting criteria under uncertainty, where existing fuzzy multi criteria group decision making (MCGDM) approaches often fail to capture asymmetric uncertainty and nonlinear interactions in expert judgments. To address this limitation, this study proposes a novel MCGDM framework based on fractional orthopair fuzzy sets (FOFS). The FOFS structure enables flexible and precise modeling of uncertainty by allowing independent fractional control of membership degree (MD) and non-membership degree (NMD). Furthermore, sine trigonometric aggregation operators are introduced to capture nonlinear relationships and fluctuations in expert evaluations. An integrated FOFS–TOPSIS method is then developed to rank candidate models based on their distances from positive ideal solution (PIS) and negative ideal solution (NIS). The applicability of the framework is demonstrated through a numerical study involving fifteen predictive models, fifteen evaluation criteria, and three experts. The results indicate that Alternative \(\:{{\rm\:A}}_{1}\) achieved the highest overall ranking, followed by \(\:{{\rm\:A}}_{15}\), while mid and lower ranked models revealed trade-offs in accuracy, computational efficiency, and robustness. Comparative and sensitivity analyses confirm the framework’s robustness, stability, and superior ranking performance.