Novel Probability Based Similarity Measure of Pythagorean Fuzzy Sets and Its Application in Clustering

This paper extends the probabilistic similarity measure from Intuitionistic Fuzzy Sets (IFSs) to Pythagorean Fuzzy Sets (PFSs), which offer a more flexible framework for modeling uncertainty. We define a new similarity measure specifically for PFSs and construct a corresponding similarity matrix to capture the relationships among PFS based data. Based on this, we propose a novel method for determining the l-cut of the equivalence relation derived from the similarity matrix. This leads to the development of a new clustering algorithm that leverages the equivalence relation on PFSs to identify meaningful clusters. The proposed algorithm is evaluated using datasets appropriate for PFS modeling and is compared with existing fuzzy clustering methods. Experimental results show that our approach performs better in terms of clustering representation.