In view of the unsure attribute weights problem of triangular fuzzy number-based uncertain multi-attribute decision making, four new equivalent definitions of triangular fuzzy numbers comparison possibility degree are proposed, and some good nature results are obtained. Learning the idea of min-max algorithm rules in the cooperative game theory, a method of determining the attribute weight based on the possibility degree of triangular fuzzy number comparison relation is proposed. Then the overall measured values of comparison possibility degree of the various alternatives are utilized to determine the best and sort the decision-making alternatives set, and an algorithm of comparison possibility degree relation for triangular fuzzy number-based uncertain multiple attribute decision making is presented. Finally, a numerical example illustrates the feasibility and effectiveness of the proposed algorithm.