A new approach to avoid rank reversal cases in the TOPSIS method

During recent decades, different methods of Multicriteria Decision Support have been used to help decision-makers select better alternatives for various decision problems. However, these methods have been criticized in the literature because they present a problem called rank reversal. In particular, analyzing this problem in relation to the TOPSIS method is still limited. Our review of the literature showed that papers are limited to analyzing cases of rank reversal by adding and removing alternatives and the solutions proposed are limited to case studies and can be improved in order to widen the scope of their application. Thus, we initially performed an analysis to determine the main cases of the rank reversal presented in the literature and to identify the main gaps in relation to the TOPSIS method. Next, we define a framework for evaluating both the TOPSIS method and the proposed model in relation to different cases of rank reversal. Finally, this paper puts forward a new method called R-TOPSIS, which proved to be robust in the experiments performed, since there were no cases of rank reversal for either the simulated cases nor for the real case used to validate it. The proposed method was also validated using statistics of dispersion and similarity to evaluate its adherence to the classic TOPSIS method.