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Multivalued Functions Integration: from Additive to Arbitrary Non-negative Set Function

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On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 336))

Abstract

It is given a short overview of some integrals of multifunctions based on additive measures, as strong, Aumann and Aumann-Gould integrals. It is considered also a multi-valued Choquet integral based on a multisubmeasure. Then it is introduced a set-valued Gould type integral of multifunctions with values in the family of all nonempty bounded subsets of a real Banach space X and with respect to an arbitrary non-negative set function. There are given some basic properties of the integrable multifunctions, and some continuity properties of the multimeasure induced by set-valued integral.

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Acknowledgments

This research was supported by the grant MNPRS 174009 and by the project “Mathematical models of intelligent systems and their applications” which was supported by the Provincial Secretariat for Science and Technological Development of Vojvodina.

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Authors and Affiliations

  1. Singidunum University, Danijelova 32, 11000, Belgrade, Serbia

    Endre Pap

  2. Óbuda University, Becsi út 92, Budapest, 1034, Hungary

    Endre Pap

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  1. Dept of Knowledge-Based Math. Systems, Johannes Kepler University Linz, Linz, Austria

    Susanne Saminger-Platz

  2. Dept. of Mathematics & Descriptive Geo., Slovak University of Technology, BRATISLAVA, Slovakia

    Radko Mesiar

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Pap, E. (2016). Multivalued Functions Integration: from Additive to Arbitrary Non-negative Set Function. In: Saminger-Platz, S., Mesiar, R. (eds) On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory. Studies in Fuzziness and Soft Computing, vol 336. Springer, Cham. https://doi.org/10.1007/978-3-319-28808-6_15

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  • DOI: https://doi.org/10.1007/978-3-319-28808-6_15

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