From MCDA to fuzzy MCDA: Presumption of model adequacy or is every fuzzification of an mCDA method justified?

Abstract

A fuzzy extension of a Multi-Criteria Decision Analysis (MCDA) method implies a choice of an approach to estimating corresponding functions of fuzzy variables and a method for ordering alternatives based on ranking of fuzzy quantities. The objective of this paper is the development and comparison of Fuzzy MCDA (FMCDA) models, which represent different approaches to fuzzy extensions of an ordinary MCDA method. To do so, different approaches to assessing functions of fuzzy numbers are considered along with several methods for ranking of fuzzy numbers. Distinctions in ranking alternatives, including the number and significance of distinctions based on a granulation of the output information, are explored for different FMCDA models by using Monte Carlo simulating input scenarios of fuzzy multi-criteria problems. In addition, both intra-distinctions and inter-distinctions are explored. According to the results, distinctions in ranking alternatives by different FMCDA models may be considered as significant both for ranking and choice multi-criteria problematiques. This research is of fundamental and applied importance and has no analogues.