Multi-person Decision Making Based on Triangular Fuzzy Preference Relations

Abstract

A multi-person decision making (MPDM) model is proposed when the experts evaluate their opinions through triangular fuzzy numbers. First, it is pointed out that the preference relations with triangular fuzzy numbers are inconsistent in nature. In order to distinguish the typical consistency, the concept of Lukasiewicz Transitivity consistency is proposed for triangular fuzzy matrices. The properties of triangular fuzzy numbers are studied in detail. Second, using preference values, a triangular fuzzy preference relation with Lukasiewicz Transitivity consistency is constructed. Third, a novel compatibility degree among triangular fuzzy preference relations is defined. There is a selection phase to rank all the alternatives for choosing the best of them. Finally, a new algorithm for the multi-person decision making problem with triangular fuzzy preference relations using Lukasiewicz Transitivity is presented. A numerical example is carried out to illustrate the proposed definitions and algorithm.