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A geometric and game-theoretic study of the conjunction of possibility measures

Miranda, Enrique; Troffaes, Matthias C.M.; Destercke, Sébastien

A geometric and game-theoretic study of the conjunction of possibility measures Thumbnail


Authors

Enrique Miranda

Sébastien Destercke



Abstract

In this paper, we study the conjunction of possibility measures when they are interpreted as coherent upper probabilities, that is, as upper bounds for some set of probability measures. We identify conditions under which the minimum of two possibility measures remains a possibility measure. We provide graphical way to check these conditions, by means of a zero-sum game formulation of the problem. This also gives us a nice way to adjust the initial possibility measures so their minimum is guaranteed to be a possibility measure. Finally, we identify conditions under which the minimum of two possibility measures is a coherent upper probability, or in other words, conditions under which the minimum of two possibility measures is an exact upper bound for the intersection of the credal sets of those two possibility measures.

Citation

Miranda, E., Troffaes, M. C., & Destercke, S. (2015). A geometric and game-theoretic study of the conjunction of possibility measures. Information Sciences, 298, 373-389. https://doi.org/10.1016/j.ins.2014.10.067

Journal Article Type Article
Acceptance Date Oct 20, 2014
Online Publication Date Nov 13, 2014
Publication Date 2015-03
Deposit Date Sep 22, 2014
Publicly Available Date Mar 29, 2024
Journal Information Sciences
Print ISSN 0020-0255
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 298
Pages 373-389
DOI https://doi.org/10.1016/j.ins.2014.10.067
Keywords Possibility measure, Conjunction, Imprecise probability, Game theory, Natural extension, Coherence.
Related Public URLs http://arxiv.org/abs/1409.4732

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Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Information sciences. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Information sciences, 298, 2015, 10.1016/j.ins.2014.10.067.




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