Enrique Miranda
A geometric and game-theoretic study of the conjunction of possibility measures
Miranda, Enrique; Troffaes, Matthias C.M.; Destercke, Sébastien
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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