Multi-Attribute Group Decision Making Method Based on EDAS Under Picture Fuzzy Environment

Xia Li,Wenkai Zhang,Aihua Wang,Peiwu Dong,Yanbing Ju,Dawei Ju

doi:10.1109/access.2019.2943348

Abstract

Multi-attribute group decision making (MAGDM) is one of the most important research hotspots in the field of decision sciences. Many practical problems are often characterized by MAGDM. The aim of this paper is to develop a new approach for MAGDM problems, in which the attribute values take the form of picture fuzzy information, and the information about the weights of attributes and decision makers is unknown. Firstly, some picture fuzzy interaction operators are presented, such as the picture fuzzy weighted interaction averaging (PFWIA) operator, picture fuzzy ordered weighted interaction averaging (PFOWIA) operator and picture fuzzy hybrid ordered weighted interaction averaging (PFHOWIA) operator. In the meantime, some desirable properties of these operators are discussed in detail. Secondly, to get reasonable decision result, we propose a method to determine the weights of decision makers under picture fuzzy setting based on the idea of the Dice similarity measure. Thirdly, for the situations where the information about the attribute weights is partly known, we establish an optimization model to determine the attribute weights on the basis of the maximizing deviation method. Fourthly, we propose a new method to solve MAGDM problems by extending the traditional Evaluation based on Distance from Average Solution (EDAS) method. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method, and the method is verified by comparing the evaluation result with that of two existing methods.

Highlights

Multi-attribute group decision making (MAGDM) is an important branch of decision theory, which has been widely used in many fields [1]–[17]
Evaluation based on Distance from Average Solution (EDAS), originally proposed by Ghorabaee et al [38], is a novel multi-attribute decision making (MADM) method
We develop a new method to determine the objective weights of decision makers under picture fuzzy environment based on the idea of Dice similarity measure

Summary

Introduction

Multi-attribute group decision making (MAGDM) is an important branch of decision theory, which has been widely used in many fields [1]–[17]. In the practical decision process, due to the ambiguity as well as intangibility arising from human qualitative judgments, experts’ opinions could involve more types of answers: yes, abstain, no and refusal, which cannot be accurately expressed by crisp values, and even cannot be described by the fuzzy set theory [18]. The picture fuzzy set method is characterized by three functions expressing the degree of positive membership, the degree of neutral membership and the degree of negative membership. Singh [21] proposed correlation coefficients for picture fuzzy sets which consider the degree of positive membership, degree of neutral membership, degree of negative membership and the degree of refusal membership, and applied the correlation coefficients to clustering analysis under picture fuzzy environment.

Objectives

Results

Conclusion