Multi-Attribute Group Decision-Making Framework for Watershed Management Using q-Fractional Fuzzy Maclaurin Symmetric Mean Operators

Effective management and analysis of watershed systems are complicated by uncertainty arising from complex, interdependent interactions among watershed elements. This work proposes a novel and efficient decision-making model based on q-Fractional Fuzzy Sets (q-FrFS), an advanced extension of fuzzy set theory. The primary objective is to improve the representation of ambiguity and imprecision in decision-making scenarios and criteria. The Maclaurin Symmetric Mean (MSM) is used to derive several new aggregation operators, including q-Fractional Fuzzy MSM (q-FrFMSM), q-Fractional Fuzzy Weighted MSM (q-FrFWMSM), q-Fractional Fuzzy Ordered Weighted MSM (q-FrFOWMSM), and q-Fractional Fuzzy hybrid Weighted MSM (q-FrFHWMSM). The operators are applied within a multi-attribute group decision-making (MAGDM) framework to successfully incorporate expert opinions. When used to assess watershed management options, the suggested MAGDM methodology shows greater consistency, robustness, and discriminative capacity than current methods in ambiguous situations. To ensure the stability and reliability of the proposed framework, a sensitivity analysis is used. Finally, the proposed framework provides a solid and practical solution for handling challenging decision-making situations in a context of uncertainty. It could be useful in environmental management and other areas and could suggest avenues for future research to refine the model and address current limitations.