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The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions

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Belief Functions: Theory and Applications (BELIEF 2018)

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Abstract

The aim of this paper is to show that the Kantorovich problem, well known in models of economics and very intensively studied in probability theory in recent years, can be viewed as the basis of some constructions in the theory of belief functions. We demonstrate this by analyzing specialization relation for finitely defined belief functions and belief functions defined on reals. In addition, for such belief functions we consider the Wasserstein metric and study its connections to disjunctions of belief functions.

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Notes

  1. 1.

    The proof of this proposition is based on Ford-Fulkerson Theorem for the network flow problem and it is omitted because of the required format of the paper.

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Acknowledgment

This work has been supported by the grant 18-01-00877 of RFBR (Russian Foundation for Basic Research).

Author information

Authors and Affiliations

  1. National Research University Higher School of Economics, Myasnitskaya 20, 101000, Moscow, Russia

    Andrey G. Bronevich

  2. JSC “Research and Design Institute for Information Technology, Signalling and Telecommunications on Railway Transport”, Orlikov per. 5, Building 1, 107996, Moscow, Russia

    Igor N. Rozenberg

Authors
  1. Andrey G. Bronevich
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  2. Igor N. Rozenberg
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Corresponding author

Correspondence to Andrey G. Bronevich .

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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Bronevich, A.G., Rozenberg, I.N. (2018). The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions. 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_5

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  • DOI: https://doi.org/10.1007/978-3-319-99383-6_5

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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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