A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making

• Published in: International journal of intelligent systems Vol. 31; no. 9; pp. 886 - 920
• Main Author: Garg, Harish
• Format: Journal Article
• Language: English
• Published: New York Blackwell Publishing Ltd 01-09-2016; Hindawi Limited
• Subjects: Agglomeration; Decision making; Fuzzy; Fuzzy logic; Fuzzy set theory; Fuzzy sets; Intelligent systems; Operators
• ISSN: 0884-8173; 1098-111X
• DOI: 10.1002/int.21809

The objective of this article is to extend and present an idea related to weighted aggregated operators from fuzzy to Pythagorean fuzzy sets (PFSs). The main feature of the PFS is to relax the condition that the sum of the degree of membership functions is less than one with the square sum of the degree of membership functions is less than one. Under these environments, aggregator operators, namely, Pythagorean fuzzy Einstein weighted averaging (PFEWA), Pythagorean fuzzy Einstein ordered weighted averaging (PFEOWA), generalized Pythagorean fuzzy Einstein weighted averaging (GPFEWA), and generalized Pythagorean fuzzy Einstein ordered weighted averaging (GPFEOWA), are proposed in this article. Some desirable properties corresponding to it have also been investigated. Furthermore, these operators are applied to decision‐making problems in which experts provide their preferences in the Pythagorean fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, a systematic comparison between the existing work and the proposed work has been given.