For the problem of uncertain multiple criteria decision making(UMCDM) of which the attribute value is triangular fuzzy number, firstly equivalent relations between several groups comparison possibility degree formulas of triangular fuzzy numbers are studied, comparative advantage relation theories of triangular fuzzy numbers are proposed, and some good properties, relations and conclusions are obtained. Then, by using the idea of maximizing deviations algorithm rules, a triangular fuzzy number-based comparison possibility degree relation model to determine the attribute weight vector is constructed. By aggregating the comparison possibility degree values of all decision objects, the set of alternatives objects is selected and scheduled, and a new model algorithm for the possibility degree relation of triangular fuzzy number-based multiple criteria decision making objects is obtained. Finally, an example is given to illustrate the feasibility and practicability of the proposed algorithm.