An Axiomatic Utility Theory for Dempster-Shafer Belief Functions

Thierry Denoeux, Prakash P. Shenoy
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:145-155, 2019.

Abstract

The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern’s utility theory for probabilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to interval-valued utilities, and therefore, to a partial (incomplete) preference order on the set of all belief function lotteries. If the belief function reference lotteries we use are Bayesian belief functions, then our representation theorem coincides with Jaffray’s representation theorem for his linear utility theory for belief functions. We illustrate our framework using some examples discussed in the literature. Finally, we compare our decision theory with those proposed by Jaffray and Smets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-denoeux19a, title = {An Axiomatic Utility Theory for Dempster-Shafer Belief Functions}, author = {Denoeux, Thierry and Shenoy, Prakash P.}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {145--155}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/denoeux19a/denoeux19a.pdf}, url = {https://proceedings.mlr.press/v103/denoeux19a.html}, abstract = {The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern’s utility theory for probabilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to interval-valued utilities, and therefore, to a partial (incomplete) preference order on the set of all belief function lotteries. If the belief function reference lotteries we use are Bayesian belief functions, then our representation theorem coincides with Jaffray’s representation theorem for his linear utility theory for belief functions. We illustrate our framework using some examples discussed in the literature. Finally, we compare our decision theory with those proposed by Jaffray and Smets.} }
Endnote
%0 Conference Paper %T An Axiomatic Utility Theory for Dempster-Shafer Belief Functions %A Thierry Denoeux %A Prakash P. Shenoy %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-denoeux19a %I PMLR %P 145--155 %U https://proceedings.mlr.press/v103/denoeux19a.html %V 103 %X The main goal of this paper is to describe an axiomatic utility theory for Dempster-Shafer belief function lotteries. The axiomatic framework used is analogous to von Neumann-Morgenstern’s utility theory for probabilistic lotteries as described by Luce and Raiffa. Unlike the probabilistic case, our axiomatic framework leads to interval-valued utilities, and therefore, to a partial (incomplete) preference order on the set of all belief function lotteries. If the belief function reference lotteries we use are Bayesian belief functions, then our representation theorem coincides with Jaffray’s representation theorem for his linear utility theory for belief functions. We illustrate our framework using some examples discussed in the literature. Finally, we compare our decision theory with those proposed by Jaffray and Smets.
APA
Denoeux, T. & Shenoy, P.P.. (2019). An Axiomatic Utility Theory for Dempster-Shafer Belief Functions. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:145-155 Available from https://proceedings.mlr.press/v103/denoeux19a.html.

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