Maximum of entropy for belief intervals under Evidence Theory

Abstract

The Dempster-Shafer Theory (DST) or Evidence Theory has been commonly used to deal with uncertainty. It is based on the basic probability assignment concept (BPA). The upper entropy on the credal set associated with a BPA is the only uncertainty measure in DST that verifies all the necessary mathematical properties and behaviors. Nonetheless, its computation is notably complex. For this reason, many alternatives to this measure have been recently proposed, but they do not satisfy most of the mathematical requirements and present some undesirable behaviors. Belief intervals have been frequently employed to quantify uncertainty in DST in the last years, and they can represent the uncertainty-basedinformation better than a BPA. In this research, we develop a new uncertainty measure that consists of the maximum of entropy on the credal set corresponding to belief intervals for singletons. It verifies all the crucial mathematical requirements and presents good behavior, solving most of the shortcomings found in uncertainty measures proposed recently. Moreover, its calculation is notably easier than the upper entropy on the credal set associated with the BPA. Therefore, our proposed uncertainty measure is more suitable to be used in practical applications.