广义证据理论的解释

THE INTERPRETATION OF GENERALIZED EVIDENCE THEORY

本文把Ｄｅｍｐｓｔｅｒ使用的随机集合概念推广到了布尔代数上，并用这个推广了的概念讨论了信息源上的不确定性结构与假设空间上的不确定性结构之间的关系．利用这个关系，本文推广了上、下概率的概念，并用其解释了Ｇｕａｎ和Ｂｅｌｌ提出的广义证据理论，同时还证明了Ｇｕａｎ和Ｂｅｌｌ定义的条件信任函数，实际上是Ｄｅｍｐｓｔｅｒ条件规则的推广．本文的解释方法一方面拓宽了广义证据理论的内容，另一方面亦为广义证据理论的应用提供了有效的途径．

This paper generalizes the concept of random sets, which were used by Dempster, to Boolean algebra, and discusses the relationship between the uncertainty structure of information sources and the uncertainty structure of hypothesis spaces. Generalizing the concepts of upper and lower probabilities, the paper gives a kind of interpretation for the generalization of evidence theory which was defined by Guan and Bell, and proves that the conditioning belief functions defined by Guan and Bell is,in fact, a generalization of Dempster's rule of condition. The interpretation method, on the one hand, further develops the generalization of evidence theory, and on the other hand,supplies a feasible application environment for the generalization of evidence theory.