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Sizes, Super Level Measures and Integrals

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Aggregation Functions in Theory and in Practice (AGOP 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 581))

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Abstract

The concept of super level measures as a generalization of classical level measures is discussed and studied in detail. Following the developing of the theory of \(L_p\)-spaces introduced by non-additive integrals based on super level measures we discuss the integration theory modified by super level measures and we compare it with the classical approach.

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Notes

  1. 1.

    The mapping \(\frac{1}{\nu }: \mathbf {E}_{\mathrm {B}}\rightarrow [0,\infty ]\) assigns 0 if \(\nu (E)=+\infty \), assigns \(+\infty \) if \(\nu (E) = 0\) and the value \(\frac{1}{\nu (E)}\) otherwise.

  2. 2.

    By \(\mathbf{1 }_F\) we denote the characteristic function of the set F, i.e., \(\mathbf{1 }_F(x)=1\) if \(x\in F\) and \(\mathbf{1 }_F(x)=0\) otherwise.

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Acknowledgements

The author kindly acknowledges the support of the grant VVGS-2016-255, and thanks the co-authors of the paper [8] who collaborated on this research.

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Authors and Affiliations

  1. Faculty of Science, Institute of Mathematics, Pavol Jozef Šafárik University in Košice, Jesenná 5, 040 01, Košice, Slovakia

    Lenka Halčinová

Authors
  1. Lenka Halčinová
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Correspondence to Lenka Halčinová .

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Editors and Affiliations

  1. School of Informatics, University of Skövde, Skövde, Sweden

    Vicenç Torra

  2. Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  3. KERMIT Research Unit Knowledge-based Systems, Ghent University, Ghent, Belgium

    Bernard De Baets

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Halčinová, L. (2018). Sizes, Super Level Measures and Integrals. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_19

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  • DOI: https://doi.org/10.1007/978-3-319-59306-7_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59305-0

  • Online ISBN: 978-3-319-59306-7

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