Symbolic Dempster-Shafer Theory

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.