A Model for Determining Weight Coefficients by Forming a Non-Decreasing Series at Criteria Significance Levels (NDSL)

Mališa Žižović,Goran Ćirović,Boža D Miljković,Miodrag M Žižović,Dragan Pamučar

doi:10.3390/math8050745

Mališa Žižović, Goran Ćirović + Show 3 more

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https://doi.org/10.3390/math8050745

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Abstract

In this paper, a new method for determining weight coefficients by forming a non-decreasing series at criteria significance levels (the NDSL method) is presented. The NDLS method includes the identification of the best criterion (i.e., the most significant and most influential criterion) and the ranking of criteria in a decreasing series from the most significant to the least significant criterion. Criteria are then grouped as per the levels of significance within the framework of which experts express their preferences in compliance with the significance of such criteria. By employing this procedure, fully consistent results are obtained. In this paper, the advantages of the NDSL model are singled out through a comparison with the Best Worst Method (BWM) and Analytic Hierarchy Process (AHP) models. The advantages include the following: (1) the NDSL model requires a significantly smaller number of pairwise comparisons of criteria, only involving an n − 1 comparison, whereas the AHP requires an n(n − 1)/2 comparison and the BWM a 2n − 3 comparison; (2) it enables us to obtain reliable (consistent) results, even in the case of a larger number of criteria (more than nine criteria); (3) the NDSL model applies an original algorithm for grouping criteria according to the levels of significance, through which the deficiencies of the 9-degree scale applied in the BWM and AHP models are eliminated. By doing so, the small range and inconsistency of the 9-degree scale are eliminated; (4) while the BWM includes the defining of one unique best/worst criterion, the NDSL model eliminates this limitation and gives decision-makers the freedom to express the relationships between criteria in accordance with their preferences. In order to demonstrate the performance of the developed model, it was tested on a real-world problem and the results were validated through a comparison with the BWM and AHP models.

Highlights

The determination of the relative weights of criteria in multi-criteria decision-making models represents a specific problem that is inevitably accompanied by subjectivities
Bearing in mind the fact that the non-decreasing series at criteria significance levels (NDSL) model is methodologically based on an assessment of the comparative significance of criteria and satisfaction of the condition of transitivity, a comparison with the Best Worst Method (BWM) and Analytic Hierarchy Process (AHP) models is a logical step for conducting a comparison of the results and validation of the model
The mathematical formulation of the NDSL model is systematized in the second section of the paper, and an algorithm, which is implemented through seven steps, is proposed

Summary

Introduction

The determination of the relative weights of criteria in multi-criteria decision-making models represents a specific problem that is inevitably accompanied by subjectivities. This procedure is very significant, since it exerts a great influence on the final decision in the decision-making process [1]. Multi-criteria optimization methods use normalized values of weights, which meet the condition. In many models for perceiving the relative ratios of weights, non-normalized values are used in the form of whole numbers or amounts in percentages [2]. The determination of the values of criteria weights is a special problem in multi-criteria optimization, so numerous models have been developed to solve it. Special attention has been devoted to studying these models in the literature dealing with multi-criteria optimization [3,4,5,6]

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