On properties of a new decomposable entropy of Dempster-Shafer belief functions

We define entropy of belief functions in the Dempster-Shafer (D-S) theory that satisfies a compound distributions property that is analogous to the property that characterizes Shannon's definitions of entropy and conditional entropy for probability mass functions. None of the existing definitions of entropy for belief functions in the D-S theory satisfy this property. We describe some important properties of our definition, and discuss its semantics as a measure of dissonance and not uncertainty. Finally, we compare our definition of entropy with some other definitions that are similar to ours in the sense that these definitions measure dissonance and not uncertainty. Published by Elsevier Inc.