Abstract: For any two interval numbers a=[a^-,a⁺] and b=[b^-,b⁺] from different sources, comparing their sizes is one of the basic problems that the academic circles have been exploring continuously.In this paper, the possibility degree of interval number a=[a^-,a⁺] larger than interval number b=[b^-,b⁺] is defined as P{a>b}$ \buildrel \Delta \over=$P{(x,y):x>y,x∈a,y∈b}. Under the assumption that the values in interval[a^-,a⁺] and[b^-,b⁺] obey the general distribution, a new probability calculation model of interval number ranking is constructed by using the definition of two-dimensional probability space distribution. The calculation model constructed by previous scholars is revised and generalized.Based on the new calculating model of possibility degree, the previous definitions of the equality of two interval numbers are revised, and the concepts of interval number shape and so on are put forward. At the same time, the reflexivity condition of possibility degree and the comprehensive ranking method of interval numbers are further revised. The theory is applied to the multiple attribute decision making problem, and the basic decision process is given. The feasibility and rationality of the new theory and method are presented by calculating the case decision-making problem, which has a good application value.

Key words: possibility degree, interval number, triangular distribution, fuzzy decision