Refined Pythagorean Fuzzy Sets: Properties, Set-Theoretic Operations and Axiomatic Results

Abstract

Refined Pythagorean fuzzy set is the generalization of fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, refined fuzzy set, and refined intuitionistic fuzzy set as it not only bears the characteristics of these models but also addresses their limitations for real-life scenarios with sub-grades corresponding to membership and non-memberships grades. In order to equip the existing literature with conceptual framework of refined Pythagorean fuzzy sets, essential properties, set-theoretic operations, and axiomatic results are characterized with the help of numerical examples.