"Thin" Structure of Relations in MCDM Models. Equivalence of the MABAC, TOPSIS(L1) and RS Methods to the Weighted Sum Method

Abstract

This paper introduces the conceptual framework of the multi-criteria decision-making (MCDM) rank model, which embodies the integration and harmonization of the aggregation method, the weighing method, the decision matrix normalization technique, and the selection of distance metrics. This definition serves to broaden the spectrum of acceptable MCDM methodologies for problem-solving and specifiing the associated tools. A Multi-Method Model (3M) approach is employed for multi-criteria selection to enhance the reliability of the results. The methodology is outlined for adjusting the rankings of alternatives to account for the distinguishability of ratings in a particular MCDM model using the Relative Performance Indicator (RPI) of alternatives. Through RPI, four methods are established for aggregating individual characteristics of alternatives that yield identical results: Weighted Sum Model (WSM), Multi-Attributive Border Approximation area Comparison (MABAC), Technique for Order Preference by Similarity to Ideal Solutions (TOPSIS (L1)), and Ratio System approach (RS), eliminating the need to duplicate these methods in the 3M approach. A comprehensive comparison of numerous multi-criteria methods is conducted based on two lists: ranking and rating. Additionally, a method for step-by-step linear transformation of alternative ratings obtained from various MCDM models is defined, facilitating comparison and aggregation of ratings.