The Prediction of Rank Reversal in TOPSIS

The rank reversal (RR) problem occurs in that rank the all-around performance (benefit or cost) of some alternatives represented with respect to rivaling criteria. The RR in the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) occurs less than other multi-criteria decision-making (MCDM) methods. We analyze the RR of simplified TOPSIS by linear normalization method of mathematic expressions. Many past papers had researched the RR, and some studies used a virtual non-dominated alternative to being ranked first to avoid RR in the original set of alternatives. However, these given and fictious alternatives are less compelling in real world objects. In addition, some authors tried to resolve RR in specific situation of TOPSIS. Consequently, we propose a manner to analyze how the mathematic expressions of TOPSIS affects the rankings, thus appraising, predicating and avoiding the RR. In order to make clear the effect of the change on the performance in any criterion, we use a simplified TOPSIS under linear normalization in decision matrix. The variation of any criterion’s component factor will be discussed and analyzed in the specified scenarios. Some examples are supplied to interpreted the mentioned effect. This research may could be the concept, recommendation and assistance for preventing and predicting the RR in TOPSIS.