Aimming at the interval number-based uncertain multi-attribute decision making problem with unknown attribute weights, the possibility degree and comparative advantage relation theory of interval number is proposed, and some results and conclusions are derived. By learning from the idea of the min-max algorithm rules in the cooperative game theory, a possibility degree programming model is established to determine the attribute weight based on the comparative advantage relation of the interval number. Then, by utilizing the measurement information of the possibility degree matrix for the comparison of the alternatives, the overall measured value of comparative possibility degree of each alternative is gathered to filter the best or worst and sort the decision making alternatives set, and therefore an algorithm of possibility degree programming for interval number-based uncertain multi-attribute decision making is proposed. Finally, the effectiveness and practicability of the proposed model algorithm are illustrated by a numerical example.