Generalized Information Theory based on the Theory of Hints

The aggregate uncertainty is the only known functional for Dempster-Shafer theory that generalizes the Shannon and Hartley mea- sures and satis?es all classical requirements for uncertainty measures, including subadditivity. Although being posed several times in the liter- ature, it is still an open problem whether the aggregate uncertainty is unique under these properties. This paper derives an uncertainty measure based on the theory of hints and shows its equivalence to the pignistic entropy. It does not satisfy subadditivity, but the viewpoint of hints un- covers a weaker version of subadditivity. On the other hand, the pignistic entropy has some crucial advantages over the aggregate uncertainty. i.e. explicitness of the formula and sensitivity to changes in evidence. We observe that neither of the two measures captures the full uncertainty of hints and propose an extension of the pignistic entropy called hints en- tropy that satis?es all axiomatic requirements, including subadditivity, while preserving the above advantages over the aggregate uncertainty.