Abstract
AbstractFuzzy extension of a Multi-Criteria Decision Analysis (MCDA) method implies a choice of an approach to assessing corresponding functions of fuzzy variables along with a method for ordering alternatives based on ranking of fuzzy quantities. The primary objective of this contribution is the development and comparison of Fuzzy MCDA (FMCDA) models, which represent different approaches to fuzzy extension of an ordinary MCDA method. For this, three approaches to assessing functions of fuzzy numbers are considered (approximate method, standard fuzzy arithmetic, and transformation method), as well as four methods for ranking of fuzzy numbers (two defuzzification methods - centroid index and integral of means, as well as modifications of these methods, which are pairwise comparison ranking methods intended to rank dependent fuzzy numbers). In this paper, distinctions in ranking alternatives by different FMCDA models, which are fuzzy extensions of an ordinary MCDA method TOPSIS as an example, are explored with the use of Monte Carlo simulation. In addition, the significance of distinctions is explored based on a granulation of the output information. According to the studies, distinctions in ranking alternatives by different FMCDA models may be considered as significant both for ranking and choice MCDA problems. This research is original and has no analogues. KeywordsFuzzy numberExtension principleRanking methodStandard fuzzy arithmeticTransformation methodFuzzy TOPSIS
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