For the interval number-based uncertain multiple attribute decision making problem with unknown attribute weights, firstly, based on the definition of relative possibility degree of interval number, the comparative relative possibility relation theory of interval number is proposed, and some related properties are obtained. Secondly, the interval number-based decision making object relative possibility relation model (IN-DMORPRM) to determine the attribute weight based on comparative relative possibility relation is established by drawing lessons from the idea of the algorithm of maximizing deviation models. Then, by aggregating and fusing the information of the relative possibility degree relation matrix measured by the superiority comparison in pairs between the decision making objects, the value of overall relative possibility degree of each decision making object is obtained, and the selection and judgment of the advantages and disadvantages of the objects set for selecting are carried out, so as to propose a new model algorithm for the relative possibility degree relation of interval number-based multi-attribute decision making objects. Finally, an numerical example is used to verify the effectiveness and practicability of the model algorithm.