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Sheffer Stroke Fuzzy Implications

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

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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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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Correspondence to Michał Baczyński .

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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

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