An Extended Step-Wise Weight Assessment Ratio Analysis with Symmetric Interval Type-2 Fuzzy Sets for Determining the Subjective Weights of Criteria in Multi-Criteria Decision-Making Problems

Mehdi Keshavarz-Ghorabaee,Jurgita Antucheviciene,Maghsoud Amiri,Zenonas Turskis,Edmundas Zavadskas

doi:10.3390/sym10040091

Mehdi Keshavarz-Ghorabaee, Jurgita Antucheviciene + Show 3 more

Open Access

https://doi.org/10.3390/sym10040091

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Abstract

Determination of subjective weights, which are based on the opinions and preferences of decision-makers, is one of the most important matters in the process of multi-criteria decision-making (MCDM). Step-wise Weight Assessment Ratio Analysis (SWARA) is an efficient method for obtaining the subjective weights of criteria in the MCDM problems. On the other hand, decision-makers may express their opinions with a degree of uncertainty. Using the symmetric interval type-2 fuzzy sets enables us to not only capture the uncertainty of information flexibly but also to perform computations simply. In this paper, we propose an extended SWARA method with symmetric interval type-2 fuzzy sets to determine the weights of criteria based on the opinions of a group of decision-makers. The weights determined by the proposed approach involve the uncertainty of decision-makers’ preferences and the symmetric form of the weights makes them more interpretable. To show the procedure of the proposed approach, it is used to determine the importance of intellectual capital dimensions and components in a company. The results show that the proposed approach is efficient in determining the subjective weights of criteria and capturing the uncertainty of information.

Highlights

In discrete multi-criteria decision-making (MCDM) processes, we are usually faced with a set of alternatives that need to be evaluated with respect to a set of criteria
The Step-wise Weight Assessment Ratio Analysis (SWARA) method is an efficient method for determination of subjective weights of criteria
Because we are usually confronted with imprecise information given by decision-makers, we need a tool that can be able to handle the uncertainty of information

Summary

Introduction

In discrete multi-criteria decision-making (MCDM) processes, we are usually faced with a set of alternatives that need to be evaluated with respect to a set of criteria. Deveci et al [43] proposed an interval type-2 fuzzy TOPSIS method to deal with multi-criteria decision-making problems under uncertainty To verify their method, a case study of airline route selection in Turkey was presented by them. Qin et al [46] developed a new approach to handle multi-criteria group decision-making problems under interval type-2 fuzzy environment Their method is based on the LINMAP (Linear Programming Models with the Aid of Multidimensional Analysis of Preference) method and they showed the application of it in supplier selection problems. Wu et al [50] developed a new methodology based on the TOPSIS method to handle large scale group decision making problems with social network information in an interval type-2 fuzzy environment They demonstrated the feasibility of the methodology using an illustrative example.

Methodology

Concepts and Definitions

An Extended SWARA with Symmetric IT2FSs

Illustrative Example

Conclusions