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On Functions Derived from Fuzzy Implications

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 610))

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Abstract

Recently, fuzzy implications based on copulas, i.e. probabilistic implications and probabilistic S-implications, were introduced and their properties were explored. However, the reverse problem of copulas derived from fuzzy implications, suggested by Massanet et al. [11, 12], is also of interest. In the paper we consider geometric properties of those fuzzy implications that generate copulas. Moreover, we consider the reverse problem for some generalizations of copulas like quasi-copulas and semi-copulas.

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References

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Author information

Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Przemysław Grzegorzewski

  2. Faculty of Mathematics and Computer Science, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland

    Przemysław Grzegorzewski

Authors
  1. Przemysław Grzegorzewski
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Corresponding author

Correspondence to Przemysław Grzegorzewski .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Machine Intelligence Institute, Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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© 2016 Springer International Publishing Switzerland

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Grzegorzewski, P. (2016). On Functions Derived from Fuzzy Implications. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 610. Springer, Cham. https://doi.org/10.1007/978-3-319-40596-4_36

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  • DOI: https://doi.org/10.1007/978-3-319-40596-4_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40595-7

  • Online ISBN: 978-3-319-40596-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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