Fuzzy TOPSIS: Violation of basic axioms

摘要

The use of fuzzy numbers (FNs) for uncertainty treatment within Multi-Criteria Decision Analysis (MCDA) is a claiming approach for examination of multicriteria problems in fuzzy environment. For proper use of a fuzzy extension for the MCDA method (FMCDA), the fulfilment of corresponding axioms/requirements, associated with this method, should be analyzed. For empirical MCDA methods (e.g., TOPSIS, AHP, PROMETHEE) the basic axiom concerns the properties of generalized criterion for this method. The goal of this contribution is exploring violation of basic axioms for FMCDA methods for Fuzzy TOPSIS (FTOPSIS) as an example. The ways of adjustment of fuzzy MCDA methods to correct use is briefly discussed.