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Dempster–Shafer belief structures with interval valued focal weights

Dempster–Shafer belief structures provide a useful framework for the representation of information about a variable whose value is uncertain. Important parameters in these structures are the weights associated with the focal elements. These weights, which can be viewed as probabilities, are required to be precisely known. Here we relax this requirement and we consider the situation in which our knowledge of the weights associated with the focal elements is that they lie in some known interval rather then being precisely specified. This relaxation will allow us to more realistically model situations in which the weights cannot be precisely obtained. At a formal level, this situation can be viewed as one in which we have some uncertainty as to what is the actual belief structure, this uncertainty being of the possibilistic type. We introduce the measures of plausibility and belief in this environment. We also look at the issue of combining belief structures for these interval type belief structures. © 2001 John Wiley & Sons, Inc.