非均匀分布下区间数排序可能度计算模型及其应用

区间数排序的可能度计算模型是学术界一直在不断探索的基础性问题之一。区间数刻画着事物属性特征的取值范围,以往学术界都假设在区间内的取值服从均匀分布。本文将均匀分布推广到一般分布,运用概率论的方法,构建了一个新的区间数排序的可能度计算模型,由此修正了以往关于两个区间数全等的定义,提出了区间数形等的概念,同时进一步修正了可能度的自反性条件和区间数的综合排序方法,并将理论应用于多属性决策问题,给出了基本的决策过程,通过实例决策问题的计算,呈现了新理论和新方法的可行性和合理性,具有很好的推广应用价值。

A Possibility Degree Model for Ranking Interval Numbers under Non-uniform Distribution and its Application

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.