Abstract
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.