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General Geometry of Belief Function Combination

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Belief Functions: Theory and Applications (BELIEF 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11069))

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Abstract

In this paper we build on previous work on the geometry of Dempster’s rule to investigate the geometric behaviour of various other combination rules, including Yager’s, Dubois’, and disjunctive combination, starting from the case of binary frames of discernment. Believability measures for unnormalised belief functions are also considered. A research programme to complete this analysis is outlined.

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Notes

  1. 1.

    For Dempster’s rule can be extended to pseudo belief functions.

  2. 2.

    We write m(x) instead of \(m(\{x\})\), \(Bel_x\) rather than \(Bel_{\{x\}}\) to simplify the notation.

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Author information

Authors and Affiliations

  1. Oxford Brookes University, Oxford, UK

    Fabio Cuzzolin

Authors
  1. Fabio Cuzzolin
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Correspondence to Fabio Cuzzolin .

Editor information

Editors and Affiliations

  1. University of Technology of Compiègne, Compiègne Cedex, France

    Sébastien Destercke

  2. UMR CNRS 7253 Heudiasyc, Université de Technologie de Compiègne, Compiègne Cedex, France

    Thierry Denoeux

  3. Department of Computing and Communication, Oxford Brookes University, Oxford, United Kingdom

    Fabio Cuzzolin

  4. Université de Rennes 1, Lannion Cedex, France

    Arnaud Martin

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Cuzzolin, F. (2018). General Geometry of Belief Function Combination. In: Destercke, S., Denoeux, T., Cuzzolin, F., Martin, A. (eds) Belief Functions: Theory and Applications. BELIEF 2018. Lecture Notes in Computer Science(), vol 11069. Springer, Cham. https://doi.org/10.1007/978-3-319-99383-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-99383-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99382-9

  • Online ISBN: 978-3-319-99383-6

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