Multiple Attribute Group Decision-Making Methods Based on Trapezoidal Fuzzy Two-Dimensional Linguistic Partitioned Bonferroni Mean Aggregation Operators.

Kedong Yin,Benshuo Yang,Xuemei Li

doi:10.3390/ijerph15020194

Abstract

In this paper, we investigate multiple attribute group decision making (MAGDM) problems where decision makers represent their evaluation of alternatives by trapezoidal fuzzy two-dimensional uncertain linguistic variable. To begin with, we introduce the definition, properties, expectation, operational laws of trapezoidal fuzzy two-dimensional linguistic information. Then, to improve the accuracy of decision making in some case where there are a sort of interrelationship among the attributes, we analyze partition Bonferroni mean (PBM) operator in trapezoidal fuzzy two-dimensional variable environment and develop two operators: trapezoidal fuzzy two-dimensional linguistic partitioned Bonferroni mean (TF2DLPBM) aggregation operator and trapezoidal fuzzy two-dimensional linguistic weighted partitioned Bonferroni mean (TF2DLWPBM) aggregation operator. Furthermore, we develop a novel method to solve MAGDM problems based on TF2DLWPBM aggregation operator. Finally, a practical example is presented to illustrate the effectiveness of this method and analyses the impact of different parameters on the results of decision-making.

Highlights

Multiple attribute group decision making (MAGDM) is the process where the decision makers select the optimal alternative from all of the predefined alternatives by comparative analysis in terms of multiple attributes variables
BM operator, and we propose trapezoidal fuzzy two-dimensional linguistic partitioned Bonferroni mean (TF2DLPBM) and trapezoidal fuzzy two-dimensional linguistic weighted partitioned Bonferroni mean (TF2DLWPBM) aggregation operators for solving MAGDM problems
We have developed a new method for solving MADGM in a fuzzy 2-dimensional linguistic environment

Summary

Introduction

Multiple attribute group decision making (MAGDM) is the process where the decision makers select the optimal alternative from all of the predefined alternatives by comparative analysis in terms of multiple attributes variables. In the fact decision-making process, decision makers are often trapped in using real number to evaluate alternatives, because the objective things are difficult to describe, and people’s judgments are subjective and uncertain. Elements like appearance, quality, portability and system fluency are taken into consideration when we determined to buy a laptop. Words like “convenient”, “general” and “inconvenient” are used to justify the portability of laptops, while in description of the system fluency, “fast” and “slow” are selected [1,2,3,4,5,6,7]. Zadeh [8,9,10,11]

Methods

Discussion

Conclusion