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1-Lipschitz Aggregation Operators, Quasi-Copulas and Copulas with Given Opposite Diagonal

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Book cover Computational Intelligence, Theory and Applications

Part of the book series: Advances in Soft Computing ((AINSC,volume 33))

Abstract

Copulas with given diagonal have been studied in [4, 10]. In [2, 5, 11] smallest and greatest (quasi-)copulas with given diagonal are constructed. Both (two-dimensional) copulas and quasi-copulas are special cases of binary 1-Lipschitz aggregation operators [3, 8], and in [7] 1-Lipschitz aggregation operators with given diagonal (and the consequences for (quasi-)copulas) are investigated. We give constructions for smallest and greatest 1-Lipschitz aggregation operators with given opposite diagonal, allowing us to obtain most results for (quasi-)copulas with given opposite diagonal as special cases.

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References

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Author information

Authors and Affiliations

  1. Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz, Austria

    Erich Peter Klement

  2. Department of Mathematics, Faculty of Chemical and Food Technology, Slovak University of Technology, Bratislava, Slovakia

    Anna Kolesárová

Authors
  1. Erich Peter Klement
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  2. Anna Kolesárová
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Editor information

Editors and Affiliations

  1. Department of Computer Science 1, University of Dortmund, FB 8 Ektrotechnik FB Informatik LS Informatik I, Postfach 50 05 00, 44221, Dortmund, Germany

    Bernd Reusch

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© 2005 Springer-Verlag Berlin Heidelberg

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Klement, E.P., Kolesárová, A. (2005). 1-Lipschitz Aggregation Operators, Quasi-Copulas and Copulas with Given Opposite Diagonal. In: Reusch, B. (eds) Computational Intelligence, Theory and Applications. Advances in Soft Computing, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31182-3_52

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  • DOI: https://doi.org/10.1007/3-540-31182-3_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22807-3

  • Online ISBN: 978-3-540-31182-9

  • eBook Packages: EngineeringEngineering (R0)

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