特征化证据信任函数的证据诱导分布函数及其性质

特征化证据信任函数的证据诱导分布函数及其性质 Induced Evidence Distribution Function Specifying Belief Function in Dempster-Shafer Theory of Evidence and Its Properties 王先甲 WANG Xian\|jia 1 2 first-author 匡小新 KUANG Xiao\|xin 1 2 武汉大学系统工程研究所 武汉大学系统工程研究所 Institute of Systems Engineering,Wuhan University Institute of Systems Engineering,Wuhan University 武汉大学系统工程研究所,湖北,武汉,430072 武汉大学系统工程研究所,湖北,武汉,430072 基于基本概率分配构造了证据判断框架上的一个证据诱导分布函数 .证明了这个证据诱导分布函数是刻划基本概率分配和信任函数特征的点函数 ,并证明了这个证据诱导分布函数也是证据理论判断框架上的概率分布 ,从而在一定意义下实现了从证据理论框架到概率论框架的转化 .另外 ,还给出了这种证据诱导分布函数的基本性质 An induced evidence distribution function is constructed based on the basic probability assignment in Dempster\|Shafer theory of evidence. The belief function over the frame of discernment Θ in Dempster\|Shafer theory of evidence ,a set\|to\|point function, which is very difficult in calculations of evidence theory, is specified by the induced evidence distribution function, a point\|to\|point function. This paper also shows that the induced evidence distribution function is a probability distribution over Θ ,which is considered as a probability space at that time. Therefore, the studying pattern of probability is transformed form the studying pattern of Dempster\|Shafer theory of evidence. In addition, the properties of the induced evidence distribution function are given and discussed. DempsterShafer证据理论 基本概率分配 信任函数 证据诱导分布函数 O;O212.5 国家自然科学基金资助项目 (698740 2 9;60 2 740 4 8) 2003-01-01 2021-04-01 1