Towards explainable TOPSIS: Visual insights into the effects of weights and aggregations on rankings

Abstract

Multi-Criteria Decision Analysis (MCDA) is extensively used across diverse industries to assess and rank alternatives. Among numerous MCDA methods developed to solve real-world ranking problems, TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) remains one of the most popular choices in many application areas. TOPSIS calculates distances between the considered alternatives and two predefined ones, namely the ideal and the anti-ideal, and creates a ranking of the alternatives according to a chosen aggregation of these distances. However, interpreting the inner workings of TOPSIS is difficult, especially when the number of criteria is large. To this end, recent research has shown that TOPSIS aggregations can be expressed using the means (M) and standard deviations (SD) of alternatives, creating MSD-space, a tool for visualizing and explaining aggregations. Even though MSD-space is highly useful, it assumes equally weighted criteria, making it less applicable to real-world ranking problems. In this paper, we generalize MSD-space to arbitrary weighted criteria by introducing the concept of WMSD-space defined by what is referred to as weight-scaled means and standard deviations. We demonstrate that TOPSIS and similar distance-based aggregation methods can be successfully illustrated in a plane and interpreted even when the criteria are weighted, regardless of their number. The proposed WMSD-space offers thus a practical method for explaining TOPSIS rankings in real-world decision problems.