Artificial Intelligence
Upper and Lower Entropies of Belief Functions Using Compatible Probability Functions
ISMIS '93 Proceedings of the 7th International Symposium on Methodologies for Intelligent Systems
Information Algebras: Generic Structures for Inference
Information Algebras: Generic Structures for Inference
Uncertainty and Information: Foundations of Generalized Information Theory
Uncertainty and Information: Foundations of Generalized Information Theory
Generic Inference: A Unifying Theory for Automated Reasoning
Generic Inference: A Unifying Theory for Automated Reasoning
Toward a characterization of uncertainty measure for the dempster-shafer theory
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Measuring ambiguity in the evidence theory
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Remarks on “Measuring Ambiguity in the Evidence Theory”
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Generalized information theory for hints
International Journal of Approximate Reasoning
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The aggregate uncertainty is the only known functional for Dempster-Shafer theory that generalizes the Shannon and Hartley measures and satisfies all classical requirements for uncertainty measures, including subadditivity. Although being posed several times in the literature, 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 uncovers 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 entropy that satisfies all axiomatic requirements, including subadditivity, while preserving the above advantages over the aggregate uncertainty.