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Proceedings of the Conference of the European Society for Fuzzy Logic and Technology

International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets

EUSFLAT 2017, IWIFSGN 2017: Advances in Fuzzy Logic and Technology 2017 pp 13–24Cite as

Sheffer Stroke Fuzzy Implications

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 643))

Abstract

A new family of fuzzy implications, motivated by classic Sheffer stroke operator, is introduced. Sheffer stroke, which is a negation of a conjunction and is called NAND as well, is one of the two operators that can be used by itself, without any other logical operators, to constitute a logical formal system. Classical implication can be presented just by Sheffer stroke operator in two ways which leads to two new families of fuzzy implication functions. It turns out that one of them is mainly a subclass of QL-operations, while the other one, called in our paper as SS\(_{qq}\)-implications, is independent of other well-known families of fuzzy implications. Basic properties of Sheffer stroke implications are also analysed.

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References

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Acknowledgments

The work on this paper for Wanda Niemyska and Michał Baczyński was supported by the research project No. 2015/19/B/ST6/03259 from the National Science Centre, Poland.

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Authors and Affiliations

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

    Wanda Niemyska & Michał Baczyński

  2. Department of Mathematics, University of Bielsko-Biała, Willowa 2, 43-309, Bielsko-Biała, Poland

    Szymon Wąsowicz

Authors
  1. Wanda Niemyska
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  2. Michał Baczyński
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  3. Szymon Wąsowicz
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Corresponding author

Correspondence to Michał Baczyński .

Editor information

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. Institute of Biophysics and Biomedical Engineering, Department of Bioinformatics and Mathematical Modelling, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

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

    Maciej Krawczak

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Niemyska, W., Baczyński, M., Wąsowicz, S. (2018). Sheffer Stroke Fuzzy 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 643. Springer, Cham. https://doi.org/10.1007/978-3-319-66827-7_2

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  • DOI: https://doi.org/10.1007/978-3-319-66827-7_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66826-0

  • Online ISBN: 978-3-319-66827-7

  • eBook Packages: EngineeringEngineering (R0)

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