A group decision making approach for trapezoidal fuzzy preference relations with compatibility measure

The purpose of this paper is to develop a new compatibility for the additive trapezoidal fuzzy preference relations and utilize it to determine the optimal weights of experts in the group decision making. First, a least deviation model to obtain the priority vector of the additive trapezoidal fuzzy preference relation is provided. Then compatibility index of two additive trapezoidal fuzzy preference relations is proposed and some desirable properties are investigated. The characteristic of the new compatibility is that it uses the deviation measure between an additive trapezoidal fuzzy preference relation and its characteristic preference relation based on consistency of the preference relation, which develops a theoretic basis for the application of additive trapezoidal fuzzy preference relations in group decision making. Then, in order to determine the weights of experts in the group decision making, we propose an optimal model based on the criterion of minimizing the compatibility index. Finally, an example shows the feasibility and effectiveness of the proposed method.