Exponential-Based Similarity Measure for Pythagorean Fuzzy Sets: A Comparative Numerical Study

Abstract

In this research article, we address the issue of uncertainty by employing Pythagorean Fuzzy Sets (PFS), which serve as a generalized form of Interval Fuzzy Sets (IFS) of type 2, providing a more flexible and comprehensive framework for modeling imprecise information. PFS extends the capability of traditional fuzzy sets (FS) and IFS by incorporating a broader range of membership and non-membership degrees, constrained by the condition that the square sum of these degrees does not exceed one. To effectively capture the relationships and fundamental connectives among FS, IFS, and PFS, we utilize a system of three-sided standards and co-norms, which serve as mathematical tools for aggregating and comparing fuzzy information. In our exploration, special emphasis is placed on using S-norms that exhibit invariance across different standard settings, ensuring consistency and reliability in operations involving fuzzy constructs. Moreover, recognizing the limitations in existing similarity measures, we propose an alternative method for evaluating the similarity between two PFSs, aimed at enhancing the accuracy and interpretability of results in applications involving uncertainty modeling, decision-making, and data analysis within complex and ambiguous environments.