Abstract
The fuzzy TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution) is an attractive tool for measuring complex phenomena based on uncertain data. The original version of the method assumes that the object assessments in terms of the adopted criteria are expressed as triangular fuzzy numbers. One of the crucial stages of the fuzzy TOPSIS is selecting the fuzzy conversion scale, which is used to evaluate objects in terms of the adopted criteria. The choice of a fuzzy conversion scale may influence the results of the fuzzy TOPSIS. There is no uniform approach in constructing and selecting the fuzzy conversion scale for the fuzzy TOPSIS. The choice is subjective and made by researchers. Therefore, the aim of the article is to present a new, objective approach to the construction of fuzzy conversion scales based on Item Response Theory (IRT) models. The following models were used in the construction of fuzzy conversion scales: Polychoric Correlation Model (PM), Polytomous Rasch Model (PRM), Rating Scale Model (RSM), Partial Credit Model (PCM), Generalized Partial Credit Model (GPCM), Graded Response Model (GRM), Nominal Response Model (NRM). The usefulness of the proposed approach is presented on the example of the analysis of a survey’s results on measuring the quality of professional life of inhabitants of selected communes in Poland. The obtained results indicate that the choice of the fuzzy conversion scale has a large impact on the closeness coefficient values. A large difference was also observed in the spreads of triangular fuzzy numbers between scales based on IRT models and those used in the literature on the subject. The use of the fuzzy TOPSIS with fuzzy conversion scales built based on PRM, RSM, PCM, GPCM, and GRM models gives results with a greater range of variability than in the case of fuzzy conversion scales used in empirical research.
Highlights
IntroductionIn socio-economic research, the assessment of objects (countries, cities, and organizations) in terms of complex phenomena (sustainable development, quality of life, and quality of services) is carried out using questionnaire studies and ordinal measurement scales (most often the Likert scales)
In socio-economic research, the assessment of objects in terms of complex phenomena is carried out using questionnaire studies and ordinal measurement scales
We developed several simulations for determining the parameters of fuzzy conversion scales based on prominent Item Response Theory (IRT) models, namely, Polytomous Rasch
Summary
In socio-economic research, the assessment of objects (countries, cities, and organizations) in terms of complex phenomena (sustainable development, quality of life, and quality of services) is carried out using questionnaire studies and ordinal measurement scales (most often the Likert scales). The first proposal in this area was the fuzzy TOPSIS method [6], whose criteria values can be expressed as fuzzy numbers. It is a useful modification for the analysis of complex socio-economic phenomena as it enables the measurement of these phenomena using fuzzy scales or fuzzy conversion scales. These are scales in which individual categories are most often expressed in triangular or trapezoidal fuzzy numbers.
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