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Extensions of Capacities

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

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

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Abstract

We study extensions of capacities on \(N=\{1,\ldots ,n\}\) to n-ary aggregation functions acting on \([0, 1]^{n}\). Besides recalling the universal integral based approaches following the ideas of Klement et al. and generalizations of the Lovász and Owen extensions, we also present some new approaches to extending such capacities which are based on a generalization of the formulas for the discrete Choquet and Sugeno integrals.

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Acknowledgments

This work was supported by the project APVV–14–0013.

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Authors and Affiliations

  1. Faculty of Chemical and Food Technology, Slovak University of Technology in Bratislava, Radlinského 9, 812 37, Bratislava 1, Slovakia

    Anna Kolesárová

  2. Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Radlinského 11, 810 05, Bratislava 1, Slovakia

    Andrea Stupňanová

Authors
  1. Anna Kolesárová
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  2. Andrea Stupňanová
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Corresponding author

Correspondence to Anna Kolesárová .

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Editors and Affiliations

  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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Kolesárová, A., Stupňanová, A. (2016). Extensions of Capacities. 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_11

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  • DOI: https://doi.org/10.1007/978-3-319-28808-6_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28807-9

  • Online ISBN: 978-3-319-28808-6

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