The extended TODIM method under q-rung orthopair fuzzy environment and its application to multi-path parallel...

Decision-making for engineering systems like multi-path parallel transmission is plagued by ambiguous and asymmetric information. While q-rung orthopair fuzzy sets offer expressive power, their decision-making frameworks face three intertwined gaps: (1) existing ranking methods yield unstable results under varying parameter q; (2) conventional distance measures fail to preserve higher-order structural information; (3) the prospect theory-based TODIM method, crucial for modeling risk-prone decisions, remains underdeveloped in q-rung orthopair fuzzy environments. To bridge these gaps, this paper introduces an integrated TODIM extension for q-rung orthopair fuzzy information. The core innovations are threefold. We first develop a geometric visualization-based ranking method that maps q-rung orthopair fuzzy numbers onto a coordinate plane and uses arc-length aggregation to integrate membership, non-membership, and hesitation degrees. This method inherently enhances interpretability and ranking stability against q-value fluctuations. Second, we propose a novel higher-order distance measure specifically designed to capture the nuanced structural information of q-rung orthopair fuzzy numbers, ensuring higher fidelity in difference quantification. Third, we seamlessly embed these enhanced components into the classical TODIM framework, creating the first comprehensive q-rung orthopair fuzzy TODIM method that retains behavioral realism while processing complex fuzzy information. A case study on multi-path transmission scheme selection demonstrates the method's practicality. Comparative experiments and a detailed sensitivity analysis confirm that our framework delivers superior ranking consistency and robustness compared to existing q-rung orthopair fuzzy MCDM methods.