Dempster-Shafer structures with general measures

We look at the transformation of information via mappings under various types of uncertainties associated with the input and output variables. We first look at mappings in which the input uniquely determines the output and investigate how various types of uncertain input information reflect into the output variable. Here, we use a measure representation for our input variable uncertainty. We next consider the case where we have an additional uncertainty in the output of the mapping, instead of it being a unique value it is a set of possible values. The special case we see here is the Dempster-Shafer belief structure. We further generalize the situation by allowing our knowledge of the output of the mapping to be expressed in terms of a measure theoretic formulation. Here, we provide a very general formulation for second-order uncertainties.