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Modeling, Design, and Simulation of Systems with UncertaintiesCoherent Upper and Lower Conditional Previsions Defined by Hausdorff Outer and Inner Measures

Modeling, Design, and Simulation of Systems with Uncertainties: Coherent Upper and Lower... [A new model of coherent upper conditional previsions is proposed to represent uncertainty and to make previsions in complex systems. It is defined by the Choquet integral with respect to Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension. Otherwise, when the conditioning event has Hausdorff outer measure equal to zero or infinity in its Hausdorff dimension, it is defined by a 0-1 valued finitely, but not countably, additive probability. If the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension, it is proven that a coherent upper conditional prevision is uniquely represented by the Choquet integral with respect to the upper conditional probability defined by Hausdorff outer measure if and only if it is monotone, comonotonically additive, submodular and continuous from below.Moreover sufficient conditions are given such that the upper conditional previsions satisfy the disintegration property and the conglomerability principle.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Modeling, Design, and Simulation of Systems with UncertaintiesCoherent Upper and Lower Conditional Previsions Defined by Hausdorff Outer and Inner Measures

Part of the Mathematical Engineering Book Series (volume 3)
Editors: Rauh, Andreas; Auer, Ekaterina
Doria, Serena
Modeling, Design, and Simulation of Systems with Uncertainties — May 13, 2011
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References (34)

Publisher
Springer Berlin Heidelberg
Copyright
© Springer-Verlag Berlin Heidelberg 2011
ISBN
978-3-642-15955-8
Pages
175 –195
DOI
10.1007/978-3-642-15956-5_9
Publisher site
See Chapter on Publisher Site

Abstract

[A new model of coherent upper conditional previsions is proposed to represent uncertainty and to make previsions in complex systems. It is defined by the Choquet integral with respect to Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension. Otherwise, when the conditioning event has Hausdorff outer measure equal to zero or infinity in its Hausdorff dimension, it is defined by a 0-1 valued finitely, but not countably, additive probability. If the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension, it is proven that a coherent upper conditional prevision is uniquely represented by the Choquet integral with respect to the upper conditional probability defined by Hausdorff outer measure if and only if it is monotone, comonotonically additive, submodular and continuous from below.Moreover sufficient conditions are given such that the upper conditional previsions satisfy the disintegration property and the conglomerability principle.]

Published: May 13, 2011

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