BMW-TOPSIS: A generalized TOPSIS model based on three-way decision

Abstract

TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) uses a pair of a positive ideal solution and a negative ideal solution as two reference points to rank a set of decision alternatives. In some situations, a trade-off of the distances to the two extreme reference points may not necessarily be meaningful. Inspired by the theory of three-way decision as thinking in threes (e.g., two opposite poles and a third middle), in this paper we generalize the classical TOPSIS by adding a third middle reference point. We use a common setting for investigating systematically reference-point-based TOPSIS-style multi-criteria decision-making methods. In particular, we examine three classes of approaches: a) a best reference point based model (i.e., B-TOPSIS) and a worst reference point based model (i.e., W-TOPSIS), b) the classical best and worst reference points based model (i.e., BW-TOPSIS), and c) a new best, mean, and worst reference points based model (i.e., BMW-TOPSIS). The three classes are one-way TOPSIS, two-way TOPSIS, and three-way TOPSIS, respectively. Based on one-way and two-way TOPSISs, we give two specific methods of three-way TOPSIS. The experimental results, compared with the existing TOPSIS methods, show that the BMW-TOPSIS model is feasible and effective.