Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)

Towards an Axiomatization for the Generalization of the Kullback-Leibler Divergence to Belief Functions

Authors
Hélène Soubaras
Corresponding Author
Hélène Soubaras
Available Online August 2011.
DOI
https://doi.org/10.2991/eusflat.2011.28How to use a DOI?
Keywords
Dempster-Shafer theory of belief functions, channel capacity, Kullback-Leibler divergence
Abstract
In his information theory, Shannon [1] defined a notion of uncertainty, the entropy, which has been generalized in several wways to belief functions [2]. He also defined the channel capacity for which we propose in this paper the first generalization to belief functions. To do that, we need first to generalize the Kullback-Leibler (KL) divergence, for which the present work proposes some axioms. Their list is still not exhaustive since the proposed solution is not unique. But there are many practical interests, since the notion of channel capacity is useful to characterize and optimize for example systems of sensors; its generalization to belief functions allows us to include imprecise sensors such as the human. Finally we show an example of gradient algorithm to compute the generalized channel capacity.
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Proceedings
Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology
Part of series
Advances in Intelligent Systems Research
Publication Date
August 2011
ISBN
978-90-78677-00-0
ISSN
1951-6851
DOI
https://doi.org/10.2991/eusflat.2011.28How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Hélène Soubaras
PY  - 2011/08
DA  - 2011/08
TI  - Towards an Axiomatization for the Generalization of the Kullback-Leibler Divergence to Belief Functions
BT  - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 1090
EP  - 1097
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.28
DO  - https://doi.org/10.2991/eusflat.2011.28
ID  - Soubaras2011/08
ER  -