Item response theory models for the fuzzy topsis in the analysis of survey data

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.