New Similarity Measures of Pythagorean Fuzzy Sets and Their Applications

Abstract

Similarity measure, as a tool to measure the similarity degree between two objects, is an important research content in fuzzy set theory. Pythagorean fuzzy set, as a new extension of fuzzy set theory, has been widely used in various fields. It is very necessary to study the similarity measure of the Pythagorean Fuzzy set. Considering that the existing similarity measures cannot distinguish the highly similar but inconsistent Pythagorean fuzzy sets and the calculation results are error-prone in application, this paper introduces the exponential function to propose several new similarity measures of the Pythagorean fuzzy set. Firstly, on the premise of introducing the existing similarity measures, several new similarity measures are defined and their properties are discussed, and then the weighted similarity measures are defined. Then, the new similarity measures and the existing similarity measures are compared by an example, and it is verified that the new similarity measures can effectively distinguish highly similar but inconsistent Pythagorean fuzzy sets. Finally, through three simulation cases, it is verified that the new similarity measures can deal with different practical application problems more accurately and reliable than the existing similarity measures.