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Article Dans Une Revue Information Sciences Année : 2013

On the connection between probability boxes and possibility measures

Résumé

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.
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Dates et versions

hal-00765618 , version 1 (15-12-2012)

Identifiants

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Matthias M.C.M Troffaes, Enrique Miranda, Sébastien Destercke. On the connection between probability boxes and possibility measures. Information Sciences, 2013, 224 (1), pp.88-108. ⟨10.1016/j.ins.2012.09.033⟩. ⟨hal-00765618⟩
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