Generalized Dempster-Shafer Structures

We review the Dempster-Shafer (D-S) belief structure and discuss the measures of plausibility and belief and other measures that can be associated with this uncertainty modeling structure. We provide a view of the D-S structure as a two-step process, the first is the selection of one of the focal elements and the second is the selection of an object from the chosen focal element. The selection of the focal element is uncertain, the uncertainty is based on a probability distribution. Here, we provide a generalization of this model by allowing a more general type uncertainty, a monotonic set measure, to model the underlying uncertainty associated with the selection of the focal element. We look at form of the plausibility and belief in this more general case. We provide a procedure for uncertain decision making when our uncertainty is modeled using this more general D-S belief structure.