According to the multi-criteria decision making problems in which the criteria and their weights take forms of the triangular fuzzy numbers, a triangular valued fuzzy VIKOR(FVIKOR) method is proposed. Firstly, the group utility, the individual regret and the compromise solutions calculated by the arithmetic regulation directly in the FVIKOR method may violate the arithmetic regulations of triangular fuzzy numbers, i.e., the left value is less than the medium value, which is in turn less than the right value, therefore, a feasible solution of defuzzifying the triangular fuzzy numbers is proposed. Then, the optimal models to designed set the parameters of defuzzifying the triangular fuzzy numbers, and the specific steps of the FVIKOR method are presented. Finally, an example illustrates the procedures and effectiveness of the proposed method.