Evaluating Belief Structure Satisfaction to Uncertain Target Values

We describe the basic properties of the Dempster-Shafer belief structure and introduce the associated measures of plausibility and belief. We look at the role of these structures for providing a model of imprecise probabilistic information. We next consider the problem of calculating the satisfaction of target values by a variable V whose value is expressed by a belief structure. We first look at the simplest case when the target is expressed as subset of the domain of V . We then look at the situation when the target is expressed by more complex uncertain structures. Among those considered are a probability distribution, another belief structure, measure, and possibility distribution. At a formal level this paper involves the extension of the concepts of plausibility and belief associated with D-S structures from being mappings of subsets of the underlying domain of V into unit interval to be mappings of these more complex structures into the unit interval.