Miranda, Enrique and Troffaes, Matthias C. M. and Destercke, Sébastien (2015) 'A geometric and game-theoretic study of the conjunction of possibility measures.', Information sciences., 298 . pp. 373-389.
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.
|Keywords:||Possibility measure, Conjunction, Imprecise probability, Game theory, Natural extension, Coherence.|
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.1016/j.ins.2014.10.067|
|Publisher 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.|
|Date accepted:||20 October 2014|
|Date deposited:||27 October 2014|
|Date of first online publication:||13 November 2014|
|Date first made open access:||No date available|
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