A Novel Similarity Measure Based on Belief and Plausibility for Pythagorean Fuzzy Multi-Criteria Decision-Making
Keywords:
Pythagorean Fuzzy Sets, Belief and Plausibility Measures, Linguistic Variables, Multi-Criteria Decision-Making, Belief and Plausibility, Technique for Order Preference by Similarity to Ideal SolutionAbstract
Several generalizations of the Dempster-Shafer theory to fuzzy sets and intuitionistic fuzzy sets have been reported in the literature. However, no studies have extended Dempster-Shafer theory to Pythagorean fuzzy distance and Pythagorean fuzzy similarity measures. This paper proposes novel distance and similarity measures for Pythagorean fuzzy sets within the framework of belief and plausibility functions. They are core components of the Dempster-Shafer theory for managing uncertain, vague, partial, and imprecise information. The validity and applicability of the proposed measures are illustrated through numerical examples, including applications to pattern recognition and linguistic variable analysis. Building on these measures, we further develop a belief- and plausibility-based technique for order preference by similarity to ideal solution (TOPSIS) method by integrating them into TOPSIS. To assess its performance, belief- and plausibility-based TOPSIS is applied to real-world multi-criteria decision-making problems. The results confirm the robustness, practicality, and effectiveness of the proposed method within the Dempster-Shafer theory framework.
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Copyright (c) 2026 Mehboob Ali, Zahid Hussain, Sadia Inayat, Rashid Hussain (Author)
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