A generalization of entropy using Dempster-Shafer theory

This paper considers a "body of evidence" on a finite set X, determined by a "basic probability assignment" (BPA) on X. This kind of information on th e set Xis ambiguous and so, in the applications, it is important to measure the degree of uncertainty involved in each BPA. In fact, several measures of uncertainty and entropy have been formulated and investigated in the set ting of Dempster-Shafer Theory of Evidence. In this paper, we use the forma l analogy underlying many of those measures of uncertainty. This moves us t o define a family of fuzzy measures associated with each BPA. Thus, we prop ose a general formulation of the entropy of a BPA. Several known measures o f entropy (including measures of imprecision and of randomness), as well as other new measures, are subsumed under our general scheme as particular ca ses. The basic properties of all those measures of entropy are also studied .