Entropy of Belief Functions in the Dempster-Shafer Theory: A New Perspective

Abstract

We propose a new definition of entropy of basic probability assignments (BPA) in the Dempster-Shafer (D-S) theory of belief functions, which is interpreted as a measure of total uncertainty in the BPA. We state a list of five desired properties of entropy for D-S belief functions theory that are motivated by Shannon’s definition of entropy of probability functions, together with the implicit requirement that any definition should be consistent with semantics of D-S belief functions theory. Three of our five desired properties are different from the five properties described by Klir and Wierman. We demonstrate that our definition satisfies all five properties in our list, and is consistent with semantics of D-S theory, whereas none of the existing definitions do. Our definition does not satisfy the sub-additivity property. Whether there exists a definition that satisfies our five properties plus sub-additivity, and that is consistent with semantics for the D-S theory, remains an open question.