A Novel TOPSIS Method Based on Improved Grey Relational Analysis for Multiattribute Decision‐Making Problem

Abstract

Multiattribute decision-making (MADM) problem is difficult to assess because of the large number of attribute indices and the diversity of data distribution. Based on the understanding of data dispersion degree, a new grey TOPSIS method for MADM is studied. The main idea of this paper is to redefine the grey relational analysis through the dispersion of data distribution and redesign the TOPSIS by using the improved grey relational analysis. As a classical multiattribute decision analysis method, traditional TOPSIS does not consider the data distribution of the degree of dispersion and aggregation when it is compared with the optimal and worst alternative solutions. In view of the limitations of traditional TOPSIS, this paper has made two major improvements to TOPSIS. Firstly, the new grey relational analysis is applied to evaluate the grey positive relational degree between each alternative and the optimal solution and compute the grey negative relational degree between each alternative and the worst solution. Secondly, the weights of every attribute index about the optimal and worst solutions are put forward based upon the distance standard deviation and the average distance. Finally, the comprehensive grey TOPSIS is utilized to analyze the ranking of weapon selection problem. The numerical results verify the feasibility of the improved grey relational analysis and also highlight the practicability of the grey comprehensive TOPSIS.

Ingenious Solution for the Rank Reversal Problem of TOPSIS Method

“…(25) Table 5 shows the evaluation results under four TOPSIS methods, including R-TOPSIS method, the reference method [56], the classical TOPSIS method, and NR-TOPSIS method established in this paper. Figure 3 also shows the distribution of evaluation results under the four TOPSIS methods.…”

“…e problem of rank reversal in the TOPSIS method has received great attention, and different scholars have tried to find satisfactory solutions from an experimental or theoretical level [52][53][54][55][56][57]. By collecting 130 related papers published in international journals from 1980 to 2015, Aires and Ferreira provided an extensive literature review on MCDM methodologies and rank reversals, including the TOPSIS method [52].…”

“…Once the cost indicator data are encountered, it will be invalid. Based on the understanding of data dispersion degree, Yang and Wu [56] proposed a new strategy combining improved grey relational analysis and TOPSIS method and verified the controllability of order reversal in the process of case verification. In the process of evaluation, the idea of attribute variable weight was adopted with the change of evaluation knowledge.…”

Material Selection of Green Design Processes for Car Body via considering Environment Property

“…In general, these methods which aim to address the MCDM problems could be generalized into the following two types. e first type is synthetic evaluation methods, such as preference ranking organization method for enrichment evaluation (PROMETHEE) [8,9], grey relational analysis (GRA) [10][11][12], technique for order preference by similarity to ideal solution (TOPSIS) [13], ELimination and Choice Expressing the REality (ELECTRE) [14,15], Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) [16,17], AHP [18,19], best-worst method (BWM) [20], decision-making trial and evaluation laboratory (DEMATEL) [21], and grey correlation (GC) [10,22,23]. And the second one is established on the basement of lifecycle assessment (LCA) [24].…”

“…From literature review, many MCDM techniques have been developed to address the selection problem considering multiple criteria, such as preference selection index (PSI) [6], graph theory and matrix representation approach (GTMA) [7], preference ranking organization method for enrichment evaluation (PROMETHEE) [8,9], grey relational analysis (GRA) [10][11][12], technique for order preference by similarity to ideal solution (TOPSIS) [13], elimination and choice translating reality (ELECTRE) [14,15], Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) [16,17], and analytic hierarchy process (AHP) [18,19]. Moreover, the combination of these methods is the most noteworthy.…”