Satisfying uncertain targets using measure generalized Dempster-Shafer belief structures

We provide the basic formalisms associated with the classic Dempster-Shafer belief structure. We note it provides a model of uncertainty that has both a probabilistic uncertainty and imprecise component. We introduce the idea of generalized D-S belief structure, which, while still having an imprecise component has more a general measure based uncertainty. We discuss the idea of a target as a subset of some space X and an uncertain target is a collection of subsets each having a probability of being the true target. We consider the problem that an uncertain variable, whose value is known to be a generalized D-S structure satisfies the target, its value lies in the target set.