Reference : Generalized Information Theory based on the Theory of Hints
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Generalized Information Theory based on the Theory of Hints
Pouly, Marc [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SnT) >]
Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Liu, Weiru
Lecture Notes in Computer Science, 6717
European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
June 29 – July 1, 2011
School of Electronics, Electrical Engineering and Computer Science, Queen’s University
United Kingdom
[en] Generalized Information Theory ; Theory of Hints ; Dempster- Shafer Theory ; Pignistic Entropy ; Hints Entropy
[en] 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.

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