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Extension of belief functions to infinite-valued events

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Abstract

We generalise belief functions to many-valued events which are represented by elements of Lindenbaum algebra of infinite-valued Łukasiewicz propositional logic. Our approach is based on mass assignments used in the Dempster–Shafer theory of evidence. A generalised belief function is totally monotone and it has Choquet integral representation with respect to a unique belief measure on Boolean events.

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Acknowledgments

The work of the author was supported by the grant GA ČR 201/09/1891 of the Czech Science Foundation and by the Grant No.1M0572 of the Ministry of Education, Youth and Sports of the Czech Republic.

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  1. Institute of Information Theory and Automation of the ASCR, Pod Vodárenskou věží 4, 182 08, Prague, Czech Republic

    Tomáš Kroupa

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  1. Tomáš Kroupa
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Correspondence to Tomáš Kroupa.

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Kroupa, T. Extension of belief functions to infinite-valued events. Soft Comput 16, 1851–1861 (2012). https://doi.org/10.1007/s00500-012-0836-2

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  • DOI: https://doi.org/10.1007/s00500-012-0836-2

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