Evidence theory extends Bayesian probability theory by allowing for a more expressive model of subjective uncertainty. Besides standard interpretation of belief functions, where uncertainty corresponds to probability masses which might refer to whole subsets of the possibility space,
semantics can be also considered. Accordingly, a belief function can be identified with the whole set of probability mass functions consistent with the beliefs induced by the masses. Following this interpretation, a novel, set-valued, dissimilarity measure with a clear behavioral interpretation can be defined. We describe the main features of this new measure and comment the relation with other measures proposed in the literature.