Fuzzy MCDA Without Defuzzification Based on Fuzzy Rank Acceptability Analysis

Abstract

Multi-criteria decision analysis (MCDA) in the fuzzy environment needs not only in implementation of functions of fuzzy variables but also inevitably leads to ranking fuzzy quantities. The use of simplification and defuzzification methods at different stages of fuzzy MCDA (FMCDA) results in a loss of information and does not meet the concept of fuzzy decision analysis that “the decision taken in the fuzzy environment must be inherently fuzzy”. In this contribution, a new approach to FMCDA is suggested, in which fuzzy criterion values and fuzzy weight coefficients are considered as fuzzy numbers (FNs) of a general type. Ranking alternatives is based on a novel methodological approach, fuzzy rank acceptability analysis (FRAA), for ranking FNs, whose use within FMCDA forms the fuzzy multicriteria acceptability analysis (FMAA) and implements a consistent approach to fuzzy decision analysis providing both ranking alternatives and the degree of confidence for each alternative to have the corresponding rank. Properties of FRAA ranking and integration of FRAA with a fuzzy extension of MAVT (FMAVT) as an example are considered and discussed along with the overestimation problem, which can arise when implementing FMCDA. The outcomes of FMAVT application for analysis of a multicriteria problem within the case study on land-use planning are considered and compared with the results by (classical) MAVT method.