Solving Decision-Making Problems Using a Measure for Information Values Connected to the Equilibrium Points (IVEP) MCDM Method and Zakeri–Konstantas Performance Correlation Coefficient

Abstract

In this paper, a new multicriteria decision-making (MCDM) method, called a measure for information values connected to the equilibrium points (IVEP) method, and a new statistical measure for measuring the similarities of performances of MCDM algorithm outputs in a comparison process, called the Zakeri–Konstantas performance correlation coefficient, are introduced. The IVEP method uses Shannon’s entropy as the primary tool to measure the information embedded in the decision matrix in order to evaluate the decision’s options/alternatives for complex decision-making problems with a large number of criteria and alternatives. The second concept that drives the IVEP method is the equilibrium points, which signify the points in a vector space where scores for the decision’s options/alternatives are equilibrated. Instead of using linear functions to compute similarities between the data sets generated by the MCDM algorithms by the calculation of the distance using different methods, the Zakeri–Konstantas performance correlation coefficient focuses on the evaluation of the ranking performance of MCDM methods in an analytic comparison process in order to determine the degree of the similarities. The IVEP method is applied to a real-world decision-making problem—a material selection problem. A comparison analysis was performed on the results obtained from the IVEP, TOPSIS, WPM, COPRAS, and ARAS MCDM methods by the Zakeri–Konstantas performance correlation coefficient and the Hamming distance. The results of both measures revealed that the IVEP algorithm’s outputs have the highest similarity to TOPSIS outputs, among others. Nevertheless, the degree of the similarities is distinct due to the different approaches of the measures used.