Cross-Entropy and Relative Entropy of Basic Belief Assignments

Thisn paper introduces the concept of cross-entropy and relative entropy of two basic belief assignments. It is based on the new entropy measure presented recently. We prove that the cross-entropy satisfies a generalized Gibbs-alike inequality from which a generalized Kullback-Leibler divergence measure can be established in the framework of belief functions. We show on a simple illustrating example how these concepts can be used for decision-making under uncertainty.