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The Law of Contraposition and the Law of Importation for Probabilistic S-Implications

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Book cover Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 642))

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Abstract

In 2011 Grzegorzewski introduced two new families of fuzzy implication functions called probabilistic implications and probabilistic s-implications. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In this article we will focus on the law of contraposition and the law of importation for probabilistic s-implications.

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References

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Authors and Affiliations

  1. Institute of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland

    Piotr Helbin

Authors
  1. Piotr Helbin
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Correspondence to Piotr Helbin .

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Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Eulalia Szmidt

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Slawomir Zadrożny

  4. Department of Telecommunications and Information Processing, Bulgarian Academy of Sciences, Sofia, Bulgaria

    K. T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

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Helbin, P. (2018). The Law of Contraposition and the Law of Importation for Probabilistic S-Implications. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 642. Springer, Cham. https://doi.org/10.1007/978-3-319-66824-6_20

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  • DOI: https://doi.org/10.1007/978-3-319-66824-6_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66823-9

  • Online ISBN: 978-3-319-66824-6

  • eBook Packages: EngineeringEngineering (R0)

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