Exponential Similarity Measures Under q-Rung Orthopair Spherical Fuzzy Environment Application To Multi-Criteria Decision-Making

Abstract

Q-rung orthopair spherical fuzzy sets (q-RO-SFSs) extend the expressive capability of fuzzy models by incorporating satisfaction, non-satisfaction, neutrality, and hesitancy degrees under a flexible q-rung structure. In this paper, we develop a family of exponential similarity measures for q-RO-SFSs, designed to capture complex uncertainty with improved sensitivity to all four components. Weighted, average, and generalized forms of the measures are proposed, and their mathematical validity is established. The applicability of the method is illustrated through multi-criteria decision-making problems, including credit evaluation and pattern recognition. Comparative analysis with existing similarity-based approaches shows that the proposed measures provide more stable and reliable rankings, demonstrating their effectiveness for practical decision-making in uncertain environments.