Research on the Optimal Aggregation Method of Decision Maker Preference Judgment Matrix for Group Decision Making

Wei Liu,Lei Li

doi:10.1109/access.2019.2923463

Abstract

The main focus of this paper is to present a new aggregation method of judgment matrices, which is based on the optimal aggregation model and the efficient aggregation algorithm. The reciprocal elements in the decision maker judgment matrices are mapped into the corresponding points on the two-dimensional coordinates. We can express the differences between different decision makers' preferences by the Euclidean distance among these points. We use the plant growth simulation algorithm (PGSA) to obtain the optimal aggregation points which can reflect the opinions of the entire decision makers group. The aggregation matrix of decision maker preference is composed of these optimal aggregation points and the consistency test has been passed. Compared with the weighted geometric mean method (WGMM) and minimum distance method (MDM), the sum of Euclidean distances from the aggregation points to other given points in this paper is minimal. The validity and rationality of this method are also verified by the analysis and comparison of examples, which provides a new idea to solve the group decision making (GDM) problems.

Highlights

Analytic Hierarchy Process (AHP) is a hierarchical weight decision analysis method, which was proposed by Saaty to solve the group decision making (GDM) problems [1]
The major objective of this paper is to present a new aggregation method of decision maker judgment matrices, which is based on the optimal aggregation model and the efficient aggregation algorithm
The optimal aggregation points can be obtained by the optimal aggregation model and the efficient algorithm

Summary

INTRODUCTION

Analytic Hierarchy Process (AHP) is a hierarchical weight decision analysis method, which was proposed by Saaty to solve the GDM problems [1]. Compared with the WA and OWA operators, Saaty and Kearns [11] argued that the WG operator is more suitable for the assembly of the AHP judgment matrix He discussed several aggregation methods for group AHP opinions, one of which was the weighted geometric mean method (WGMM). Li: Research on the Optimal Aggregation Method of Decision Maker Preference Judgment Matrix for GDM advocated the use of the WGM for the aggregation in AHP. In order to improve the additive consistency and make up for the missing elements in incomplete HFPR, Zhang et al [28], [29] proposed the new approach and models to solve these problems Most of these methods are extended or mixed by using WA,OWA,WG,PG operators, etc. In order to achieve the goals, we map the reciprocal elements of each decision maker judgment matrix in the AHP into the corresponding points on the two-dimensional coordinates. The expert judgment matrices of (1) are mapped to the set of plane points of (2), which signifies that the aggregation of the expert judgment matrices is transformed into the aggregation of the two-dimensional coordinates points

THE OPTIMAL AGGREGATION MODEL Definition1

PLANT GROWTH SIMULATION ALGORITHM

CORE PROCESS FOR SEARCHING OPTIMAL

NUMERICAL ANALYSIS

EXAMPLE 2

CONCLUSION AND SUGGESTIONS FOR