A robust method for avoiding rank reversal in the TOPSIS

Abstract

The ability to obtain robust ranking results is an important reference factor when choosing a method for multiple criteria decision-making (MCDM). However, the rank reversal phenomenon of MCDM makes its credibility greatly compromised, as represented by the technique for order preference by similarity to ideal solution (TOPSIS). Although some research papers have presented interesting ideas and solutions to minimize/void rank reversal in relation to the TOPSIS, there are still some gaps that need further research, such as do not utterly eliminate the rank reversal, need more additional decision information, cannot theoretically guarantees the stability of ranking. Therefore, an improved TOPSIS method, named IE-TOPSIS, is developed based on information expansion and virtual ideal points. An algorithm for the extreme value extension of criteria indicators is initially constructed, based on the existing decision-making information, which can effectively avoid the influence of the data standardization process on decision-making ranking. And then, the concept of a virtual ideal point is proposed, which can prevent the rank reversal caused by the change of ideal points in varying decision-making environments. At the same time, this paper proves that the IE-TOPSIS satisfies ranking stable according to the given definition of ranking robust, which theoretically guarantees that the rank reversal phenomenon does not exist. In the case where the IE-TOPSIS is established, a new ranking index is proposed that can better distinguish the evaluation objects and solve the problem that the classic TOPSIS ranking index cannot completely rank the decision objects. Finally, in the verification of examples, the ranking results show that the improved TOPSIS has strong consistent with the theoretical analysis, and is robust to handle rank reversal phenomenon in all the scenarios in comparison with other studies available in the literature.