Modeling positive and negative pieces of evidence in uncertainty

Abstract

In Dempster-Shafer theory, belief degrees on any subset A ⊂ Ω of states of nature are computed through a basic belief mass m(A), that quantifies the strength of the statement: "the agent has some reason to believe that the true world is in A". We may be interested into representing some negative belief, as for example: "the agent has some reason not to believe that the true world is in A". However, as remarked by Smets, this is not allowed in the theory of Dempster-Shafer. Attempts to model this situation have been proposed by Smets, and by Dubois, Prade and Smets in the framework of possibility theory. These solutions however, do not seem to be able to handle all the facets of the problem, and have the drawback to come up with an interval or a pair of values. In this paper, we propose an alternative solution consisting in assigning a single number to a pair of events.