Abstract
Belief functions and reachable probability intervals are theories based on imprecise probabilities that generalize classical probability theory. On the one hand, belief functions have been commonly used to deal with uncertainty and in the combination of information provided by different sources. On the other hand, reachable probability intervals have high expressive power, are easy to manage, and can be efficiently computed. Belief functions are not generalizations of reachable probability intervals, and the converse is also not verified. In this work, we study under which conditions a reachable set of probability intervals is associated with a belief function, as well as the properties that a belief function has to satisfy to be representable by a reachable set of probability intervals.
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