A modified TOPSIS method with rationality and consistency in ranking decision

Technique for order preference by similarity to ideal solution (TOPSIS) is a popular approach in multiple attribute decision-making. It ranks by estimating the separations between alternatives and the positive ideal solution (PIS) as well as the negative ideal solution (NIS). When setting the ranking rules, there are three limitations to the TOPSIS. First, there is controversy surrounding the addition of negative and positive indicators in the denominator of the ranking index, as these measurements represent opposite aspects. Second, the ranking index is also irrespective of the relative magnitudes of the distances from alternatives to PIS and NIS, resulting in incomparable situations. Third, the ranking results derived from the distances to PIS, the distances to NIS, and the relative closeness are inconsistent. To address these limitations, this paper first analyzes the inconsistency through a spatial partition diagram, that helps access the possible results under different indexes. Then, we define strong, weak, and no priority relationships between alternatives based on the differences in the distances to PIS and NIS, making the comparability enhanced. For further incorporating their differences in ranking, we also generate a relationship matrix based on the priority relationships from one alternative to all other alternatives, and devise a new, rational ranking index to address the non-additivity debate. Simulations and numerical example of a real-life case are conducted to demonstrate the rationality and superiority of the modified TOPSIS.