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On the Analysis of Probability-Possibility Transformations: Changing Operations and Graphical Models

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Book cover Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9161))

Abstract

Representing and reasoning with uncertain information is a common topic in Artificial Intelligence. In this paper, we focus on probability-possibility transformations in the context of changing operations and graphical models. Existing works mainly propose probability-possibility transformations satisfying some desirable properties. Regarding the analysis of the behavior of these transformations with respect to changing operations (such as conditioning and marginalization), only few works addressed such issues. This paper concerns the commutativity of transformations with respect to some reasoning tasks such as marginalization and conditioning. Another crucial issue addressed in this paper is the one of probability-possibility transformations in the context of graphical models, especially the independence of events and variables.

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Notes

  1. 1.

    \(\triangleright \) is always assumed to satisfy Dubois and Prade consistency and preference preservation principle.

  2. 2.

    Let \(\alpha \), \(\phi \) and \(\psi \) be three arbitrary events, in probability theory (resp. possibility theory ), \(\phi \) is said to be independent of \(\psi \) in the context of \(\alpha \) iff \(P(\phi |\psi ,\alpha )\)=\(P(\phi |\alpha )\) (resp. \(\varPi (\phi |\psi ,\alpha )\)=\(\varPi (\phi |\alpha )\)).

  3. 3.

    The permutation property of probability-possibility transformations is discussed in [18].

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Acknowledgements

This work is done with the support of a CNRS funded project PEPS FaSciDo 2015 called MAPPOS.

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Authors and Affiliations

  1. University of Lille Nord de France, 59000, Lille, France

    Salem Benferhat, Amélie Levray & Karim Tabia

  2. UArtois, CRIL UMR CNRS 8188, 62300, Lens, France

    Salem Benferhat, Amélie Levray & Karim Tabia

Authors
  1. Salem Benferhat
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  2. Amélie Levray
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  3. Karim Tabia
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Correspondence to Amélie Levray .

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Editors and Affiliations

  1. Université de Technologie de Compiègne, Compiègne, France

    Sébastien Destercke

  2. Centre de Recherches de Royallieu, Université de Technologie de Compiègne, Compiègne, France

    Thierry Denoeux

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Benferhat, S., Levray, A., Tabia, K. (2015). On the Analysis of Probability-Possibility Transformations: Changing Operations and Graphical Models. In: Destercke, S., Denoeux, T. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2015. Lecture Notes in Computer Science(), vol 9161. Springer, Cham. https://doi.org/10.1007/978-3-319-20807-7_25

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  • DOI: https://doi.org/10.1007/978-3-319-20807-7_25

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