Approaches to Multiple Attribute Decision Making with Interval-Valued 2-Tuple Linguistic Pythagorean Fuzzy Information

Guiwu Wei,Jie Wang,Hui Gao

doi:10.3390/math6100201

Abstract

The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among multi-input arguments. Motivated by the ideal characteristic of the MSM operator, in this paper, we expand the MSM operator, generalized MSM (GMSM), and dual MSM (DMSM) operator with interval-valued 2-tuple linguistic Pythagorean fuzzy numbers (IV2TLPFNs) to propose the interval-valued 2-tuple linguistic Pythagorean fuzzy MSM (IV2TLPFMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted MSM (IV2TLPFWMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy GMSM (IN2TLPFGMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted GMSM (IV2TLPFWGMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy DMSM (IN2TLPFDMSM) operator, Interval-valued 2-tuple linguistic Pythagorean fuzzy weighted DMSM (IV2TLPFWDMSM) operator. Then the multiple attribute decision making (MADM) methods are developed with these three operators. Finally, an example of green supplier selection is used to show the proposed methods.

Highlights

Atanassov [1,2] introduced the concept of an intuitionistic fuzzy set (IFS), which is a generalization of the concept of fuzzy set [3]
In order to overcome this issue, we propose the definition of interval-valued 2-tuple linguistic Pythagorean fuzzy sets (IV2TLPFSs) based on the IVPFSs [34] and 2-tuple linguistic sets [38,39]
The aim of this paper is to propose some Maclaurin symmetric mean (MSM) operators with IV2TLPFNs, to study some properties of these operators, and applied them to cope with the multiple attribute decision making (MADM) with IV2TLPFNs

Summary

Introduction

Atanassov [1,2] introduced the concept of an intuitionistic fuzzy set (IFS), which is a generalization of the concept of fuzzy set [3]. Each element in the IFS is expressed by an ordered pair, and each ordered pair is characterized by a membership degree and a non-membership degree. The sum of the membership degree and the non-membership degree of each ordered pair is less than or equal to 1. The PFS is characterized by the membership degree and the non-membership degree, whose sum of squares is less than or equal to 1, the PFS is more general than the IFS. Zhang and Xu [6] developed a Pythagorean fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) for handling the multiple criteria decision making (MCDM) problem within Pythagorean fuzzy numbers (PFNs). Ren et al [8] developed the Pythagorean fuzzy

Objectives

Results

Conclusion