Intuitionistic Fuzzy Synthetic Measure on the Basis of Survey Responses and Aggregated Ordinal Data.

Bartłomiej Jefmański,Ewa Roszkowska,Marta Kusterka-Jefmańska

doi:10.3390/e23121636

Bartłomiej Jefmański, Ewa Roszkowska + Show 1 more

Open Access

https://doi.org/10.3390/e23121636

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Abstract

The paper addresses the problem of complex socio-economic phenomena assessment using questionnaire surveys. The data are represented on an ordinal scale; the object assessments may contain positive, negative, no answers, a “difficult to say” or “no opinion” answers. The general framework for Intuitionistic Fuzzy Synthetic Measure (IFSM) based on distances to the pattern object (ideal solution) is used to analyze the survey data. First, Euclidean and Hamming distances are applied in the procedure. Second, two pattern object constructions are proposed in the procedure: one based on maximum values from the survey data, and the second on maximum intuitionistic values. Third, the method for criteria comparison with the Intuitionistic Fuzzy Synthetic Measure is presented. Finally, a case study solving the problem of rank-ordering of the cities in terms of satisfaction from local public administration obtained using different variants of the proposed method is discussed. Additionally, the comparative analysis results using the Intuitionistic Fuzzy Synthetic Measure and the Intuitionistic Fuzzy TOPSIS (IFT) framework are presented.

Highlights

Multiple criteria decision making (MCDM) has been an important research discipline of decision science applied in many areas such as business, management, engineering, and social science [1,2,3]
To develop a general Intuitionistic Fuzzy Synthetic Measure (IFSM) based on Hellwig’s approach for the evaluation of socioeconomic phenomena with survey data; to study the IFSM based on Hellwig’s approach taking into account two types of Euclidean and Hamming distance implemented in the procedure; to study the IFSM based on Hellwig’s approach considering two or three parameters used in distance measure applied in the procedure; to study the IFSM based on Hellwig’s approach examining different pattern object construction used in the procedure; to propose the method for criteria comparison with the Intuitionistic Fuzzy Synthetic
In the case of using the pattern object, the coordinates of which were determined based on intuitionistic values (1,0), and the Hamming distance, it did not matter whether the IFSM or the Intuitionistic Fuzzy TOPSIS (IFT) measure was used in ranking the cities (Spearman coefficient value was 1)

Summary

Introduction

Multiple criteria decision making (MCDM) has been an important research discipline of decision science applied in many areas such as business, management, engineering, and social science [1,2,3]. In another paper [21] a synthetic measure based on Hellwig’s approach and the interval-valued intuitionistic fuzzy set theory is presented. The assessment criteria are expressed in the form of three parameters of the intuitionistic fuzzy set: membership, non-membership and uncertainty The difference in these methods consists in determining values of these parameters. To develop a general IFSM based on Hellwig’s approach for the evaluation of socioeconomic phenomena with survey data; to study the IFSM based on Hellwig’s approach taking into account two types of Euclidean and Hamming distance implemented in the procedure; to study the IFSM based on Hellwig’s approach considering two or three parameters used in distance measure applied in the procedure; to study the IFSM based on Hellwig’s approach examining different pattern object construction used in the procedure; to propose the method for criteria comparison with the Intuitionistic Fuzzy Synthetic.

Preliminaries

Classical Variant of Hellwig’s Method

Problem Description and Data Source

Analysis of the Results

Comparative Analysis and Implications

Conclusions