An extended multi-attribute group decision-making method based on novel information measures and its application

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.

Interval-Valued q-Spherical Fuzzy Rough Sets and TOPSIS for Multi-Criteria Decision-Making: Application to Sustainable Smart City Development

This study develops an interval-valued q-spherical fuzzy rough set TOPSIS framework (IVq-SFRS-TOPSIS) for multi-criteria group decision-making when expert judgments contain interval uncertainty, neutrality, and granular indiscernibility. The revised framework clarifies the relationship between interval-valued q-spherical and interval-valued T-spherical fuzzy models, defines admissible approximation operators over compatible domains, and introduces a radial projection step that guarantees closure under the IVq-SFN constraint whenever component-wise extrema would otherwise violate it. The proposed framework provides a mathematically balanced representation of interval-valued q-spherical fuzzy information, reflecting the concept of symmetry and supporting reliable group decision-making under uncertainty. The TOPSIS procedure is then formulated through expert aggregation, benefit–cost normalization, entropy-based criteria weighting, ideal-solution distance calculation, and closeness-coefficient ranking. The method is illustrated through a sustainable smart city development case using four AI-based alternatives and six criteria. Rather than claiming unconditional superiority, the revised comparative and sensitivity analyses examine how the ranking changes under alternative fuzzy decision models, different q values, perturbations to criteria weights, and perturbations to the decision matrix. The results indicate that the proposed framework provides an interpretable rough-boundary representation and a reproducible ranking mechanism for complex MCDM problems under interval-valued q-spherical uncertainty.

A unified uncertainty-aware decision framework for air quality assessment

A Hamacher Aggregation-Based Pythagorean Fuzzy Z-Number MCDM Framework for Sustainable Urban Green Space Planning

Evaluation of alternatives is a complex task in real-world decision-making, where ambiguity and uncertainty are inherent. To address these challenges, this study proposes an integrated Pythagorean Fuzzy Z-Number (PyFZN)-based framework for multi-attribute decision-making (MADM) in urban green space planning. PyFZNs extend intuitionistic fuzzy sets by incorporating both fuzzy membership information and reliability measures, enabling a more realistic representation of uncertainty and a more effective modeling of expert judgments. Hamacher norms with adjustable parameters are employed to improve the aggregation process, providing greater flexibility and consistency in information fusion. Based on these norms, a family of aggregation operators is developed to enhance decision-making performance under uncertain conditions. The proposed PyFZN-MADM framework is applied to evaluate urban green space alternatives using criteria such as population coverage, accessibility, environmental impact, cost, and social benefits. A metropolitan case study demonstrates the applicability of the proposed framework for ranking alternatives, optimizing resource allocation, and improving urban livability. The results indicate that the proposed approach is robust, sensitive, and reliable, outperforming existing methods in handling uncertainty and prioritizing alternatives. Comparative analysis further confirms its effectiveness in supporting informed, consistent, and reliable decision-making in complex urban planning environments.

A new three-way decision model for multi-source interval valued fuzzy decision systems based on utility theory

A Novel Evidence-Based Framework for Picture Fuzzy Sets: Theory and Applications of Belief and Plausibility

Picture Fuzzy Sets (PiFSs) have appeared as an effective tool to tackle ambiguity in decision-making and offer greater flexibility than traditional extensions of Fuzzy Sets (FSs). Under the framework of evidence theory (ET), the concepts of belief and plausibility significantly boost the representative capacity of PiFSs, which enables the management of uncertain and ambiguous data. We constructed both distance and similarity measures specifically for Belief and Plausible Picture Fuzzy Sets (BP-PiFSs). The constructed measures detect the differences and connections between BP-PiFSs and addressed the key shortcomings in current methodologies. They are mathematically validated and applied to real-world scenarios, such as fault detection in complex systems and antenna design optimization, where managing uncertainty is critical. A modified decision-making method, Belief and Plausible SMART (BP-SMART), extends the classical SMART approach to more effectively handle multi-criteria decision-making (MCDM) in uncertain environments. Numerical evaluations across pattern recognition, clustering, fault detection, and MCDM demonstrates the effectiveness and robustness of the suggested framework, contributing significantly to both the theoretical and practical development of fuzzy set theory.