Equivalence of MCDM Methods and Synthesis of Solution Based on Ratings Obtained in Different Models

Irik Z. Mukhametzyanov; Dragan Pamucar

doi:10.31181/dmame8220251473

Authors

Irik Z. Mukhametzyanov Institute of Socio-Economic Research – subdivision of the Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa, Russia
Dragan Pamucar Széchenyi István University, Győr, Hungary

DOI:

https://doi.org/10.31181/dmame8220251473

Keywords:

MCDM; Multi-Method Model approach; Relative Performance Indicator (RPI); WSM; RS; MABAC; TOPSIS; MAIRCA; RAWEC.

Abstract

Synthesis of solutions based on a set of models is a modern trend in the field of multi-criteria choice. It is assumed that a solution based on many methods increases the reliability of the decisions made. One of the important tasks is to select an independent set of models. Comparison of various multi-criteria methods is performed using two lists: rank and rating. To compare the rating of alternatives obtained using different MCDM models, the article uses the Relative Performance Indicator (RPI). Using RPI, six identical methods for aggregating private attributes of alternatives are established: Weighted Sum Model (WSM), Ratio System approach (RS), Multi-Attributive Border Approximation area Comparison (MABAC), Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) with L₁ metric, Multi Atributive Ideal-Real Comparative Analysis (MAIRCA) and Ranking of Alternatives with Weights of Criterion (RAWEC) provided that each aggregation method combines the same method of linear normalization of attributes. This allows avoiding duplication of equivalent methods in the Multi-Method Model (3M) approach combining different MCDM models. When solving MCDM problems, it is recommended to use the simplest and most easily interpreted of them: WSM. The presented methodology is recommended as mandatory for the analysis of new or hybrid MCDM methods to eliminate duplication of existing methods. A synthesis of a solution based on ratings obtained in different MCDM models within the 3M approach is proposed. The method includes coordinating the common goal of several models and bringing the ratings obtained in different MCDM models to a common scale, which allows comparing and aggregating the ratings. The resulting rating is more informative than a rating based on ranks, such as Borda rules or similar, since it reflects the real proportions of the effectiveness of alternatives in different models.

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