Abstract: To solve the problem of uncertain multi-criteria decision-making in which the characteristic attribute is interval number and the attribute weight is completely unknown, a new decision method was proposed based on theories of probability superiority relationship. The basic principle for relationship between interval number and superiority was given, the degree of comparative advantage was defined, and the attribute of interval number was represented by the probability superiority relationship. By constructing evaluation matrix, the problem of ordering decision plans was converted into a matrix operation process. The ranking of different candidate schemes has been realized. An analysis of the example shows that the method can make full use of interval number information, overcome the limitation of traditional decision-making methods effectively, and have advantages of objective and reasonable ordering and high decision precision.

Key words: multi-criteria decision-making, degree of comparative superiority, probability superiority relationship, weight, interval number