Abstract
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.