On Similarity Measures Between Pythagorean Fuzzy Sets Derived from Overlap and Grouping Functions

In 2013, Yager introduced the theory of Pythagorean fuzzy set (PFS) to generalize the application range of fuzzy sets. Compared with fuzzy set and intuitionistic fuzzy set (IFS), PFS is more capable to handle uncertainty in the real world. Similarity measure is an important topic in the theory of PFS and has been applied in various fields, such as classification, clustering, decision making, and so on. Meanwhile, overlap and grouping functions, as two novel continuous binary aggregation functions, have been discussed in the literature for applications in image processing, decision making, classification and so on. The main purpose of this paper is to construct similarity measures between PFSs based on overlap and grouping functions. Firstly, on the basis of overlap and grouping functions, we introduce two novel construction methods of similarity measure between PFSs, called O-similarity measure and G-similarity measure, respectively. Secondly, we use some numerical examples to illustrate characteristics of O-similarity measure in detail. Finally, we show the applications of O-similarity measure in classification and clustering to demonstrate effectiveness and superiority of the proposed methods in the environment of expert assessments and data sets. The results of experiments show that O-similarity measure has better performance than some existing similarity measures under some conditions.