In view of the triangular fuzzy number-based uncertain multi-attribute decision making problem with unknown attribute weights, the new relative similarity degree of the triangular fuzzy number and decision-making alternatives are defined, and the relative similarity degree relation theory of the triangular fuzzy number is presented. Learning the idea of maximizing possibility degree algorithm rules in the cooperative game theory, an approach of determining the attribute weight based on the triangular fuzzy number relative similarity degree relation is proposed. Then the overall relative similarity degree value of the alternative objects in the alternative set is utilized to select the optimal object and sort, therefore an algorithm of relative similarity degree relation for triangular fuzzy number-based uncertain multiple attribute decision making is presented. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed algorithm.