A Context-aware Cognitive Decision-making Framework for Green Supplier Selection Using Quasi-rung Orthopair Diophantine Fuzzy Modeling

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.