区间值集函数变差的性质

Some properties of the variations of interval value set functions

为了解决不确定环境中的决策问题,采用理论分析的方法,将决策者的风险偏好引入到区间数的运算中,提出基于风险因子的区间数运算法则,在此运算法则基础上,定义了区间值集函数的变差,研究了区间值集函数不交变差的零零可加性,零可加性,穷竭性,及从下连续性等基本性质。结果表明:定义的区间值集函数的变差是对经典测度论中不交变差的自然推广,对不确定环境中的决策及建立模糊测度具有很强的指导意义。

In order to deal with the decision-making under uncertainties,the study generalizes algebraic operation to closed interval based on risk index of the decision making. Subsequently,the disjoint variation of the interval-valued set functions is established. The study will discuss some basic properties of the disjoint variation,such as （null-） null-additivity,exhaustivity,and continuity,etc. The results show that the definition of disjoint variation of interval-valued set functions is a natural extension of the disjoint variation of the classical measure theory. The study is of significance to solve uncertain problems.