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On Conditional Belief Functions in the Dempster-Shafer Theory

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Belief Functions: Theory and Applications (BELIEF 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13506))

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Abstract

The primary goal is to define conditional belief functions in the Dempster-Shafer theory. We do so similar to the notion of conditional probability tables in probability theory. Conditional belief functions are necessary for constructing directed graphical belief function models in the same sense as conditional probability tables for constructing Bayesian networks. Besides defining conditional belief functions, we state and prove a few basic properties of conditionals. We provide several examples of conditional belief functions, including those obtained by Smets’ conditional embedding.

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Notes

  1. 1.

    This phenomenon has been observed, e.g., in [11, 16], and [12]. An example is given in [10].

  2. 2.

    An example is given in [10].

  3. 3.

    If \(P_X(x) = 0\), then the conditional has no effect on the joint, and 0/0 can be left undefined, or defined as 1.

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Acknowledgments

This study was supported by the Czech Science Foundation Grant No. 19-06569S to the first two authors and by the Ronald G. Harper Professorship at the University of Kansas to the third author.

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Authors and Affiliations

  1. Faculty of Management, University of Economics, Jindřichův Hradec, Czechia

    Radim Jiroušek & Václav Kratochvíl

  2. Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czechia

    Radim Jiroušek & Václav Kratochvíl

  3. School of Business, University of Kansas, Lawrence, KS, 66045, USA

    Prakash P. Shenoy

Authors
  1. Radim Jiroušek
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  2. Václav Kratochvíl
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  3. Prakash P. Shenoy
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Corresponding author

Correspondence to Prakash P. Shenoy .

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Editors and Affiliations

  1. University of Paris-Saclay, Gif sur Yvette, France

    Sylvie Le Hégarat-Mascle

  2. Sorbonne University, Paris, France

    Isabelle Bloch

  3. University of Paris-Saclay, Gif sur Yvette, France

    Emanuel Aldea

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Jiroušek, R., Kratochvíl, V., Shenoy, P.P. (2022). On Conditional Belief Functions in the Dempster-Shafer Theory. In: Le Hégarat-Mascle, S., Bloch, I., Aldea, E. (eds) Belief Functions: Theory and Applications. BELIEF 2022. Lecture Notes in Computer Science(), vol 13506. Springer, Cham. https://doi.org/10.1007/978-3-031-17801-6_20

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  • DOI: https://doi.org/10.1007/978-3-031-17801-6_20

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  • Online ISBN: 978-3-031-17801-6

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