定性Dempster-Shafer理论

Symbolic Dempster-Shafer Theory

采用一个全序的符号值集合来代替数值信任度集合[0,1],提出定性Dempster-Shafer理论来处理既有不确定性又有不精确性的推理问题·首先,定义了适合对不确定性进行定性表达和推理的定性mass函数、定性信任函数等概念,并且研究了这些概念之间的基本关系;其次,详细讨论了定性证据合成问题,提出了基于平均策略的证据合成规则·这种定性Dempster-Shafer理论与其他相关理论相比,既通过在定性领域重新定义Dempster-Shafer理论的基本概念,继承了Dempster-Shafer理论在不确定推理方面的主要特点,同时又具有适合对不精确性操作的既有严格定义又符合直观特性的定性算子,因此更适合基于Dempster-Shafer理论框架不精确表示和处理不确定性·

Symbolic Dempster-Shafer （D-S for short） theory is presented to handling imprecise and uncertain reasoning. The numerical set of belief degrees [ 0,1 ] in classical D-S theory is replaced by a totally ordered scale of symbolic values. After the qualitative mass function and qualitative belief function are defined by qualitative operators, the fundamental relation between them is discussed. The combination of evidence in qualitative way is also discussed in detail. Compared to other related work, there are two essential characteristics of the symbolic D-S theory. One is that the theory inherits the advantages of classic D-S theory on uncertain reasoning by re-defining the essential concepts in D-S theory. Another one is that the qualitative operators involved in the approach are strictly defined by the logic formulas as well as intuitive properties. Consequently, the symbolic D-S theory is more suitable for reasoning about uncertainty and imprecision in the framework of D-S theory.