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: Oct 27, 2014
• 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.
• Public URL: https://durham-repository.worktribe.com/output/1445187
• Related Public URLs: http://arxiv.org/abs/1409.4732