Irik Z. Mukhametzyanov

6602584820

Publications - 2

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

Publication Name: Decision Making Applications in Management and Engineering

Publication Date: 2024-01-23

Volume: 7

Issue: 2

Page Range: 418-442

Description:

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.

Open Access: Yes

DOI: 10.31181/dmame7220241088

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

Publication Name: Decision Making Applications in Management and Engineering

Publication Date: 2025-01-01

Volume: 8

Issue: 2

Page Range: 1-20

Description:

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.

Open Access: Yes

DOI: 10.31181/dmame8220251473