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Symmetric coherent upper conditional prevision defined by the Choquet integral with respect to Hausdorff outer measure

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  • Serena Doria

Abstract

In a metric space symmetric fuzzy measures defined on the class of all subsets are introduced. Coherent upper conditional probabilties defined by Hausdorff outer measures are symmetric and distorted coherent upper conditional probabilities defined by Hausdorff outer measures with concave distortion are proven to be symmetric. Null events and symmetric events with respect to coherent upper conditional probabilities defined by Hausdorff outer measures are characterized. Coherent upper conditional prevision defined as Choquet integral with respect to Hausdorff outer measure is symmetric because it is invariant with respect to equimeasurable random variables. Copyright Springer Science+Business Media New York 2015

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  • Serena Doria, 2015. "Symmetric coherent upper conditional prevision defined by the Choquet integral with respect to Hausdorff outer measure," Annals of Operations Research, Springer, vol. 229(1), pages 377-396, June.
    • Handle: RePEc:spr:annopr:v:229:y:2015:i:1:p:377-396:10.1007/s10479-014-1752-x
    DOI: 10.1007/s10479-014-1752-x
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    References listed on IDEAS

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    1. Serena Doria, 2012. "Characterization of a coherent upper conditional prevision as the Choquet integral with respect to its associated Hausdorff outer measure," Annals of Operations Research, Springer, vol. 195(1), pages 33-48, May.
    2. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
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    Cited by:

    1. Serena Doria, 2019. "Preference orderings represented by coherent upper and lower conditional previsions," Theory and Decision, Springer, vol. 87(2), pages 233-252, September.
    2. Serena Doria, 2017. "On the disintegration property of coherent upper conditional prevision defined by the Choquet integral with respect to its associated Hausdorff outer measure," Annals of Operations Research, Springer, vol. 256(2), pages 253-269, September.

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