Abstract
•Discusses Basic Dempster–Shafer belief structure for modeling uncertainty.•Discusses entailment/inference of one belief structures from another.•Describes general belief structure with underling uncertainty based on measure.•Extends concept of entailment to these general measure based belief structures.•Provides concept of containment between general belief structures.
We discuss the Dempster–Shafer belief structure on finite universes and note its use for modeling variables that have both probabilistic uncertainty as well as imprecision. We note for these structures the probability that the variable lies in a subset cannot be precisely known but only be known to an interval value. We discuss methods for deducing this uncertainty interval. We next discuss the issue of entailment of belief structures, inferring the validity of additional belief model of a variable from an already established belief model of the variable. We next discuss a more general belief structure were the underling uncertainty rather tha0n being based on a probability distribution is based on a general measure type of uncertainty. We then extend the concept of entailment to the case where the belief structures are these more general measure based belief structures. In order to accomplish this we must extend the idea of containment from classic Dempster–Shafer belief structures to measure based belief structures.