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On the connection between probability boxes and possibility measures.

Troffaes, Matthias C. M. and Miranda, Enrique and Destercke, Sebastien (2013) 'On the connection between probability boxes and possibility measures.', Information sciences., 224 . pp. 88-108.


We explore the relationship between possibility measures (supremum preserving normed measures) and p-boxes (pairs of cumulative distribution functions) on totally preordered spaces, extending earlier work in this direction by De Cooman and Aeyels, among others. We start by demonstrating that only those p-boxes who have 0-1-valued lower or upper cumulative distribution function can be possibility measures, and we derive expressions for their natural extension in this case. Next, we establish necessary and sufficient conditions for a p-box to be a possibility measure. Finally, we show that almost every possibility measure can be modelled by a p-box, simply by ordering elements by increasing possibility. Whence, any techniques for p-boxes can be readily applied to possibility measures. We demonstrate this by deriving joint possibility measures from marginals, under varying assumptions of independence, using a technique known for p-boxes. Doing so, we arrive at a new rule of combination for possibility measures, for the independent case.

Item Type:Article
Keywords:Probability boxes, Possibility measures, Maxitive measures, Coherent lower and upper probabilities, Natural extension.
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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, 224, 2014, 10.1016/j.ins.2012.09.033.
Date accepted:No date available
Date deposited:17 October 2014
Date of first online publication:March 2013
Date first made open access:No date available

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