Ingenious Solution for the Rank Reversal Problem of TOPSIS Method

Although the classic TOPSIS method is very practical, there may be a problem of rank reversal in the addition, deletion, or replacement of the candidate set, which makes its credibility greatly compromised. Based on the understanding of the classical TOPSIS method, this paper establishes a new improved TOPSIS method called NR-TOPSIS. Firstly, the historical maximum and minimum values of all attribute indicators from a global perspective during the evaluation process are determined. Secondly, according to whether the attributes belong to the benefit attribute or cost attribute, standardization is carried out. And then, in the case where the historical values of attributes are determined, we re-fix the positive ideal solution and the negative ideal solution. At the same time, this paper gives the definition of ranking stable and proves that the NR-TOPSIS proposed satisfies ranking stable, which theoretically guarantees that the rank reversal phenomenon does not exist. Finally, in the verification of examples, the results are consistent with the theoretical analysis, which further support the theoretical analysis. The NR-TOPSIS method overcomes rank reversal, which is not only obviously superior to the classical TOPSIS method but also relatively superior to the R-TOPSIS method which has also overcome rank reversal. It is also superior to other reference methods due to its simple calculation.