Eliminating Rank Reversal Problem Using a New Multi-Attribute Model—The RAFSI Method

Mališa Žižović,Dragan Pamučar,Miloljub Albijanić,Prasenjit Chatterjee,Ivan Pribićević

doi:10.3390/math8061015

Abstract

Multi-attribute decision-making (MADM) methods represent reliable ways to solve real-world problems for various applications by providing rational and logical solutions. In reaching such a goal, it is expected that MADM methods would eliminate inconsistencies like rank reversal issues in a given solution. In this paper, an endeavor is taken to put forward a new MADM method, called RAFSI (Ranking of Alternatives through Functional mapping of criterion sub-intervals into a Single Interval), which successfully eliminates the rank reversal problem. The developed RAFSI method has three major advantages that recommend it for further use: (i) its simple algorithm helps in solving complex real-world problems, (ii) RAFSI method has a new approach for data normalization, which transfers data from the starting decision-making matrix into any interval, suitable for making rational decisions, (iii) mathematical formulation of RAFSI method eliminates the rank reversal problem, which is one of the most significant shortcomings of existing MADM methods. A real-time case study that shows the advantages of RAFSI method is presented. Additional comprehensive analysis, including a comparison with other three traditional MADM methods that use different ways for data normalization and testing the resistance of RAFSI method and other MADM methods to rank the reversal problem, is also carried out.

Highlights

Multi-criteria optimization (MCO) methods represent powerful tools for making rational decisions while being engaged in various types of activities
According to the results shown in this paper, three main advantages of the RAFSI method distinguish it from the other traditional Multi-attribute decision-making (MADM) methods, which include (1) a simple algorithm of RAFSI method that enables DMs to solve complex problems, (2) use a new data normalization technique that converts an initial decision matrix into a unique criterion interval, and (3) resistance of the RAFSI method to rank reversal problems
We can conclude that rank reversal problems exist in Complex Proportional Assessment (COPRAS), TOPSIS, and Više Kriterijumska optimizacija i Kompromisno Rešenje (VIKOR) methods can lead to irrational results in conditions where we have changeable initial parameters in the decision matrix

Summary

Introduction

Multi-criteria optimization (MCO) methods represent powerful tools for making rational decisions while being engaged in various types of activities. According to the results shown in this paper, three main advantages of the RAFSI method distinguish it from the other traditional MADM methods, which include (1) a simple algorithm of RAFSI method that enables DMs to solve complex problems, (2) use a new data normalization technique that converts an initial decision matrix into a unique criterion interval, and (3) resistance of the RAFSI method to rank reversal problems We are emphasizing this phenomenon since it can be especially seen in dynamic conditions of decision-making where some alternatives often change during the process of making decisions, and MADM methods are often used in such conditions.

Alternatives

Case Study and Results

Comparing the Results with Other MADM Methods

Rank Reversal Problem

Discussion and Conclusions