Enhancing VIKOR for MAGDM with PUIL q-ROFSs: Addressing Ambiguity and Uncertainty in Decision-Making

Effectively evaluating educational curricula requires capturing experts’ nuanced linguistic judgments, which often exhibit probabilistic uncertainty and cognitive asymmetry that existing fuzzy models struggle to represent. This study addresses the critical challenge of processing such unbalanced and probabilistic linguistic information in multi-attribute group decision-making (MAGDM) by proposing probabilistic unbalanced interval linguistic q-Rung orthopair fuzzy sets (PUIL q-ROFSs). This novel framework integrates unbalanced double-hierarchy linguistic term sets with interval-valued q-ROFSs to capture expert evaluations more naturally and flexibly. Our core contributions include developing a comprehensive theoretical foundation with specialized distance measures, operational rules for PUIL q-ROFSs, and an expanded VIKOR (Vise Kriterijumska Optimizacija I Kompromisno Resenje) method that effectively reconciles attribute conflicts to identify balanced compromise solutions. In a case study on curriculum evaluation, the proposed method demonstrated superior practicality and reliability over existing models, successfully translating complex linguistic assessments into a robust decision-making framework for improving educational quality.