A New Index for TOPSIS based on Relative Distance to Best and Worst Points

The technique for order performance by similarity to ideal solution (TOPSIS) is one of the most well-known methods in multiple criteria decision making (MCDM) problems. The classical TOPSIS method employs a similarity index to rank alternatives. However, the chosen alternative sometimes does not have the shortest distance to the positive ideal solution (PIS) and remotest distance from the negative ideal solution (NIS), simultaneously. Besides, in some cases, TOPSIS cannot assign a unique rank to alternatives. The purpose of this paper is to propose a new similarity TOPSIS index based on the relative distance to the best and worst points. In the proposed method, by treating the separations of an alternative from the PIS and the NIS as negative criterion and positive criterion, respectively, we reduce the original MCDM problem to a new one with two criteria. The proposed index, based on different weights, in optimistic, pessimistic, and apathetic cases, easily determines the score of each alternative. Finally, we illustrate the proposed index using four numerical examples. The results are compared with those published in the literature.