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Multi-Criteria Decision Analysis (MCDA) is extensively used across diverseindustries to assess and rank alternatives. Among numerous MCDA methodsdeveloped to solve real-world ranking problems, TOPSIS remains one of the mostpopular choices in many application areas. TOPSIS calculates distances betweenthe considered alternatives and two predefined ones, namely the ideal and theanti-ideal, and creates a ranking of the alternatives according to a chosenaggregation of these distances. However, the interpretation of the innerworkings of TOPSIS is difficult, especially when the number of criteria islarge. To this end, recent research has shown that TOPSIS aggregations can beexpressed using the means (M) and standard deviations (SD) of alternatives,creating MSD-space, a tool for visualizing and explaining aggregations. Eventhough MSD-space is highly useful, it assumes equally important criteria,making it less applicable to real-world ranking problems. In this paper, wegeneralize the concept of MSD-space to weighted criteria by introducing theconcept of WMSD-space defined by what is referred to as weight-scaled means andstandard deviations. We demonstrate that TOPSIS and similar distance-basedaggregation methods can be successfully illustrated in a plane and interpretedeven when the criteria are weighted, regardless of their number. The proposedWMSD-space offers a practical method for explaining TOPSIS rankings inreal-world decision problems.

Towards Explainable TOPSIS: Visual Insights into the Effects of Weights and Aggregations on Rankings