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

We propose a new definition of entropy for 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. Our definition is different from the definitions proposed by H¨ohle, Smets, Yager, Nguyen, Dubois-Prade, Lamata-Moral, Klir-Ramer, Klir-Parviz, Pal et al., MaedaIchihashi, Harmanec-Klir, Jousselme et al., and Pouly et al. 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 for probability functions together with the requirement that any definition should be consistent with the semantics of D-S belief functions theory