Some Complex Pythagorean Fuzzy Einstein Geometric Aggregation Operators and their Application in Decision-Making Process

Abstract

The goal of this research is to introduce some Einstein aggregation operators for aggregating the different complex Pythagorean fuzzy sets (CPFSs) by considering the dependency between the pairs of its membership degrees. In the existing studies of fuzzy and its extensions, the uncertainties present in the data are handled with the help of degrees of membership that are the subset of real numbers, which may also loss some valuable data and hence consequently affect the decision results. A modification to these, complex Pythagorean fuzzy set handles the uncertainties with the degree whose ranges are extended from real subset to the complex subset with unit disc and hence handle the two dimensional information in a single set. Thus, motivated by this and this paper we present some novel Einstein aggregation operators, namely complex Pythagorean fuzzy Einstein weighted geometric (CPFEWG) aggregation operator, complex Pythagorean fuzzy Einstein ordered weighted geometric (CPFEOWG) aggregation operator, complex Pythagorean fuzzy Einstein hybrid geometric (CPFEHG) aggregation operator, induced complex Pythagorean fuzzy Einstein ordered weighted geometric (I-CPFEOWG) aggregation operator, and induced complex Pythagorean fuzzy Einstein hybrid geometric (I-CPFEHG) aggregation operator. Also develop some of their desirable properties. Furthermore, based on these proposed aggregation operators a multi-attribute group decision making problems developed under complex Pythagorean fuzzy set environment. An illustrative example related to the selection of the best alternative is considered to show the effectiveness, importance and efficiency of the new developed approach.