Abstract
As a new extension of Pythagorean fuzzy set (also called Atanassov’s intuitionistic fuzzy set of second type), interval-valued Pythagorean fuzzy set which is parallel to Atanassov’s interval-valued intuitionistic fuzzy set has recently been developed to model imprecise and ambiguous information in practical group decision making problems. The aim of this paper is to put forward a novel decision making method for handling multiple criteria group decision making problems within interval-valued Pythagorean fuzzy environment based on interval-valued Pythagorean fuzzy numbers (IVPFNs). There are three key issues being addressed in this approach. The first is to introduce an interval-valued Pythagorean fuzzy weighted arithmetic averaging (IVPF-WAA) operator to aggregate the decision data in order to get the overall preference values of alternatives. Some desirable properties of the IVPF-WAA operator are also investigated. Based on the idea of the maximizing deviation method, the second is to establish an optimization model for determining the weights of criteria for each expert. The third is to construct a minimizing consistency optimal model to derive the weights of criteria for the group. Finally, an illustrating example is given to verify the proposed approach.
Highlights
Fuzzy set originally introduced by Zadeh [1] in 1965 is a useful tool to capture the imprecision and uncertainty in decision making [2, 3]
Considering the fact that interval-valued Pythagorean fuzzy numbers (IVPFNs) have great powerful ability to model the imprecise and ambiguous information in real-world applications [18], this paper develops a maximizing deviation method based on interval-valued Pythagorean fuzzy weighted average aggregating (IVPF-WAA) operator to solve multiple criteria group decision making (MCGDM) problems with IVPFNs
Compared with the IVPF-TOPSIS approach, the proposed method does not require experts to provide the weights of criteria in advance, but it constructs two optimal models to determine objectively the weights, which avoids the subjective randomness of selecting the weights of criteria
Summary
Fuzzy set originally introduced by Zadeh [1] in 1965 is a useful tool to capture the imprecision and uncertainty in decision making [2, 3]. In human cognitive and decision making activities, it is not completely justifiable or technically sound to quantify the degrees of the membership and nonmembership in terms of a single numeric value [16, 17] To this end, Zhang [18] further extended the PFSs to propose the concept of interval-valued PFSs (IVPFSs) which is parallel to Atanassov’s intervalvalued intuitionistic fuzzy set [19, 20]. Considering the fact that IVPFNs have great powerful ability to model the imprecise and ambiguous information in real-world applications [18], this paper develops a maximizing deviation method based on interval-valued Pythagorean fuzzy weighted average aggregating (IVPF-WAA) operator to solve MCGDM problems with IVPFNs. We first present the concept of the score and accuracy functions for IVPFNs, and we further present a score and accuracy functions-based ranking method for comparing the magnitude of IVPFNs. we employ the maximizing deviation method to determine the weights of criteria for each expert.
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