Decision-making in uncertain and dynamic environments often requires models capable of accurately representing both expert disagreement and incomplete information. This paper proposes a comprehensive decision-making framework based on the Quasi-Rung Orthopair Diophantine Fuzzy (QRODF) set, which extends existing fuzzy theories by introducing five adjustable parameters \(p, q, \rho, \varrho\) and \(\:\sigma\:\) to model optimism, hesitation, and rejection with high flexibility. The fundamental operations and properties of the QRODF set are formally defined, and two aggregation operators, namely the QRODF Weighted Averaging (QRODFWA) and QRODF Weighted Geometric (QRODFWG) operators, are developed to integrate multi-expert evaluations and criteria. The Analytic Hierarchy Process (AHP) and entropy weighting methods are adapted to the QRODF environment to ensure dynamic and context-aware weight assignment. The proposed model is validated through a green supplier selection problem involving five alternatives, five criteria, and three experts. Results demonstrate strong performance with a decision accuracy of 97.8%, ranking stability of 98.6%, and an average computation time of 0.82 s, confirming both robustness and scalability. Comparative analysis shows that traditional fuzzy, intuitionistic fuzzy, and \(\:q-\)rung orthopair fuzzy models are less stable and adaptable under uncertainty. Overall, this study contributes a mathematically rigorous and practically effective framework for complex multi-criteria decision-making, offering valuable applications in sustainable manufacturing and intelligent supply chain management.

This study introduces a novel distance measure (DM) for spherical fuzzy sets (SFSs) to improve decision-making in complex and uncertain environments. Many existing distance measures either fail to satisfy essential axiomatic ... | Find, read and cite all the research you need on Tech Science Press

The Hamy mean (HM) operator is a powerful parameterized aggregation tool that enables flexible modeling of both conjunctive and disjunctive decision-making behaviors within a unified mathematical framework. Its tunable nature makes it more versatile than traditional fixed aggregation operators such as the arithmetic mean, maximum, or minimum, which are often too rigid to capture the nuanced interactions among decision criteria. Despite its proven potential in other fuzzy environments, the HM operator has not yet been developed in the context of p, q − quasirung orthopair fuzzy (p, q − QOF) sets, a generalized and more expressive extension of orthopair fuzzy models that can handle higher degrees of uncertainty, vagueness, and hesitation. To address this gap, we introduce some novel aggregation operators: the p, q − QOF interaction weighted Hamy mean (p, q − QOFIWHM) and the p, q − QOF interaction weighted dual Hamy mean (p, q − QOFIWDHM) operators. The proposed operators inherit the parametric adaptability of the HM while incorporating the enhanced representational capabilities of p, q − QOF sets. This combination offers significant flexibility in capturing interrelationships among criteria, making the operators well-suited for complex, large-scale, and time-sensitive decision problems. Based on these operators, we develop a multicriteria group decision-making (MCGDM) framework capable of effectively managing heterogeneous expert opinions, uncertain information, and high-dimensional evaluation data. The applicability and effectiveness of the proposed approach are demonstrated through a comprehensive case study on an E-Learning Platform selection. In this study, assessments from three domain experts were considered for 20 candidate platforms evaluated against 20 criteria encompassing technical, pedagogical, usability, and security aspects, such as system performance, course management capabilities, adaptability of learning content, cost-effectiveness, user interface quality, scalability, and data security. A detailed sensitivity analysis of parameters \(p\) and q, as well as of criteria weights, was conducted to examine the robustness of the model. Furthermore, extensive stability and accuracy tests revealed that the proposed approach consistently outperformed existing aggregation operator-based methods, achieving superior accuracy (93.13%), stability (98.83%), and computational efficiency. Comparative analysis confirmed that the p, q − QOFIWHM and p, q − QOFIWDHM-based MCGDM framework not only improves decision reliability but also provides a scalable and adaptable tool for real-world decision-making scenarios.

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.