Applications of Weighted Tangent Similarity Measure of Picture Hesitant Fuzzy Sets (European Journal of Pure and Applied Mathematics, 2025)
Picture hesitant fuzzy sets (PHFSs) provide a powerful framework for modeling uncertainty by incorporating the degrees of membership, non-membership, neutrality, and refusal. This paper introduces a novel similarity measure, the Weighted Tangent Similarity Measure (ωTSM), designed to improve sensitivity to subtle variations and to capture nonlinear interactions amongPHFS components. The proposed measure is theoretically established and empirically validated through two real-world decision-making problems: medical diagnosis and building material classification. In both cases, ωTSM effectively distinguishes between closely related alternatives and consistently outperforms existing methods. The comparative analysis highlights its robustness,flexibility, and practical value in environments characterized by ambiguity and hesitation. Overall, this study advances fuzzy decision-making models and provides a foundation for future applications in knowledge representation and intelligent systems.
Keywords: \keywords{Picture hesitant fuzzy set; Tangent similarity measure; Weighted tangent similarity measure; Medical diagnosis; Building material recognition}