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Propagation of Belief Functions in Singly-Connected Hybrid Directed Evidential Networks

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Scalable Uncertainty Management (SUM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9310))

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Abstract

Directed evidential networks (DEVNs) can be seen, at present, as an extremely powerful graphical tool for representing and reasoning with uncertain knowledge in the framework of evidence theory.

The main purpose of this paper is twofold. Firstly, it introduces hybrid directed evidential networks which generalize the standard DEVNs. Secondly, it presents an algorithm for performing inference over singly-connected hybrid evidential networks.

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Notes

  1. 1.

    In Bayesian networks, conditional probabilities are specified per child node, i.e. for each node given all its parents. However, in ENCs, if there are two edges going from nodes A and B to their common child node C, then two conditional belief function distributions have to be defined: a distribution for C given A and another one for C conditionally to B.

  2. 2.

    The notations m[N\(_\mathrm{{k}}\)](N\(_\mathrm{{i}}\)) and m\(^{{\small \mathrm{{N}}_\mathrm{{i}}}}[{\small \mathrm{{N}}_\mathrm{{k}}}]\) used throughout this paper correspond to the classical notation m(N\(_\mathrm{{i}}\) \(\mid \)N\(_\mathrm{{k}}\)).

  3. 3.

    Case 1 occurs when the child node \({\mathrm{{N}}_\mathrm{{i}}}\) is associated with conditionals specified per single parent.

  4. 4.

    Case 2 occurs when the child node \({\mathrm{{N}}_\mathrm{{i}}}\) has one conditional distribution defined for all its parents.

  5. 5.

    Case 3 occurs when \({\mathrm{{N}}_\mathrm{{j}}}\) has one or more child nodes associated with conditionals specified per single parent.

  6. 6.

    Case 4 occurs when \({\mathrm{{N}}_\mathrm{{j}}}\) has one or more child nodes associated with conditionals specified for all the parents.

References

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Author information

Authors and Affiliations

  1. LARODEC Laboratory - Institut Supérieur de Gestion de Tunis, Tunis, Tunisia

    Wafa Laâmari & Boutheina Ben Yaghlane

Authors
  1. Wafa Laâmari
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  2. Boutheina Ben Yaghlane
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Corresponding author

Correspondence to Wafa Laâmari .

Editor information

Editors and Affiliations

  1. Fakultät für Mathematik und Informatik, FernUniversität in Hagen, Hagen, Germany

    Christoph Beierle

  2. California Polytechnic State University, SAN LUIS OBISPO, USA

    Alex Dekhtyar

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Laâmari, W., Ben Yaghlane, B. (2015). Propagation of Belief Functions in Singly-Connected Hybrid Directed Evidential Networks. In: Beierle, C., Dekhtyar, A. (eds) Scalable Uncertainty Management. SUM 2015. Lecture Notes in Computer Science(), vol 9310. Springer, Cham. https://doi.org/10.1007/978-3-319-23540-0_16

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  • DOI: https://doi.org/10.1007/978-3-319-23540-0_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23539-4

  • Online ISBN: 978-3-319-23540-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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