Ordering the chaos of sustainable supply chains: A q-rung fuzzy hypersoft framework for multi-attribute green supplier selection

This study proposes a decision-making framework for green supplier selection in sustainable supply chain management under high uncertainty and expert hesitancy, particularly in contexts where evaluation criteria possess hierarchical sub-attributes. A multi-attribute group decision-making approach is developed using q-rung orthopair fuzzy hypersoft sets (q-ROFHSS) integrated with Frank t-norm and t-conorm based aggregation. Two aggregation operators, namely q-ROFHSFWA (weighted averaging) and q-ROFHSFWG (weighted geometric), are introduced to fuse expert assessments and derive final supplier evaluations using a q-ROFHS score function. A case study involving four candidate suppliers and four evaluation criteria is presented to illustrate the applicability of the proposed method. The results indicate that supplier rankings vary across aggregation behaviors, with q-ROFHSFWA yielding the ranking F3 > F2 > F1 > F4, while q-ROFHSFWG produces the ranking F2 > F1 > F3 > F4. Sensitivity analysis demonstrates that rankings remain stable within each aggregation operator for multiple values of the q parameter and exhibit controlled variation under different Frank parameter sigma values, highlighting the flexibility of the proposed framework. By combining hypersoft modeling with Frank-based aggregation, the proposed approach preserves sub-attribute information, accommodates diverse risk attitudes, and enhances transparency in green supplier selection under uncertainty.