In the classical Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method, rank reversal is a significant issue. When adding, deleting, or replacing alternatives, it may lead to changes in the relative rankings of each alternative. This phenomenon undermines the credibility of the decision-making process and introduces significant risks in practical applications where reliability is of critical importance. To address this issue, this paper proposes a new boxplot-based TOPSIS method (BP-TOPSIS). The BP-TOPSIS redefines both the normalization process and the construction of ideal solutions by incorporating boxplot principles to extend extreme values, thereby mitigating ranking inconsistencies caused by changes in the alternative. The specific improvements include: (1) The extended extremum method based on boxplot analysis that does not require assumptions about data distribution, making it suitable for arbitrarily distributed criteria; (2) A new max-min normalization approach and fixed virtual ideal solutions to enhance stability; (3) An evaluation index for rank reversal based on the inversion number is proposed. Numerical analyses and random experiments demonstrate that the rank reversal rate of BP-TOPSIS is significantly lower than that of both classical TOPSIS and the improved TOPSIS (IE-TOPSIS) method. A case study further shows that BP-TOPSIS produces results highly consistent with other Multi-Criteria Decision-Making (MCDM) techniques, including Simple Additive Weighting (SAW) and VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), thereby providing a more reliable and stable solution for complex MCDM problems.
Yang et al. (Thu,) studied this question.