On the axiomatic requirement of range to measure uncertainty

How to measure uncertainty is still an open issue. Probability theory is a primary tool to express the aleatoric uncertainty. The Shannon's information entropy is an effective measure for the uncertainty in probability theory. Dempster-Shafer theory, an extension of probability theory, has the ability to express the aleatoric and epistemic uncertainty, simultaneously. With respect to such uncertainties in Dempster-Shafer theory, a justifiable uncertainty measure is required to satisfy five axiomatic requirements based on previous studies. In this paper, we show that one of the axiomatic requirements, the requirement of range, is questionable. The correct range of uncertainty should be [0,log₂2^|X|] rather than [0,log₂|X|] according to the concept of entropy.