Reversão de ordem no método Technique for Order Preference by Similarity to Ideal Solution - TOPSIS

Abstract

During the last decades, various multi-criteria decision-making methods (MCDM) have been used to assist decision makers in selecting the best alternatives for many decision problems. Among them, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is one of the most used. Despite its wide dissemination, it has been criticized due to the occurrence of a problem called rank reversal, which in its most known meaning refers to the change in the ordering of a group of previously ordered alternatives after an irrelevant alternative has been added or removed from this group. Despite the significant amount of research on this problem for MCDM methods, it has been superficially analyzed in the case of TOPSIS, without a careful study on the occurrence causes and conditions, as well as marked by propositions inadequate models. Therefore, the aim of this study was to propose an extension of the TOPSIS method to minimize rank reversal. For this, it was realized an experimental research through computer simulations randomly generated based on four reversal situations selected in the literature. In the cases of the both problems types investigated, of choice and rank, the effects of the normalization used and the indifference thresholds were analyzed. In addition, the cases of the problem of choice were also analyzed from the logistic regression, in order to estimate the conditions in which there is a greater probability of occurrence of rank reversal. Based on the experiments and analysis of the literature models, an extension of TOPSIS was proposed. The proposed model is based on the definition of a set of values called Domain, which represents the limit values of each criterion in the decision matrix in order to overcome the drawbacks of TOPSIS. For the validation of the proposal, a numerical application was made for the problem of student selection and it was concluded that the proposed model is robust because it simultaneously prevents the occurrence of ranking reversal and presents a good discriminatory capacity.