A group decision making model based on triangular fuzzy additive reciprocal matrices with additive approximation-consistency

A group decision making (GDM) 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 additive approximation-consistency is proposed for triangular fuzzy additive reciprocal matrices. The properties of triangular fuzzy additive reciprocal matrices with additive approximation-consistency are studied in detail. Second, using (n − 1) restricted preference values, a triangular fuzzy additive reciprocal preference relation with additive approximation-consistency is constructed. Third, a novel compatibility degree among triangular fuzzy additive reciprocal preference relations is defined. It is further applied to introduce the compatibility-degree induced ordered weighted averaging (CD-IOWA) operator for generating a collective triangular fuzzy additive reciprocal matrix with additive approximation-consistency. Finally, a new algorithm for the group decision-making problem with triangular fuzzy additive reciprocal preference relations is presented. A numerical example is carried out to illustrate the proposed definitions and algorithm.