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On Fuzzy Sheffer Stroke Operation

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Artificial Intelligence and Soft Computing (ICAISC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10842))

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Abstract

The generalization of the classical logical connectives to the fuzzy logic framework has been one of the main research lines since the introduction of fuzzy logic. Although many classical logical connectives have been already generalized, the Sheffer stroke operation has received scant attention. This operator can be used by itself, without any other logical operator, to define a logical formal system in classical logic. Therefore, the goal of this article is to present some initial ideas on the fuzzy Sheffer stroke operation in fuzzy logic. A definition of this operation in the fuzzy logic framework is proposed. Then, a characterization theorem in terms of a fuzzy conjunction and a fuzzy negation is presented. Finally, we show when we can obtain other fuzzy connectives from fuzzy Sheffer stroke operation.

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References

  1. Baczyński, M., Jayaram, B.: Fuzzy Implications. Studies in Fuzziness and Soft Computing, vol. 231. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69082-5

    Book  MATH  Google Scholar 

  2. Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)

    Book  Google Scholar 

  3. Klement, E., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)

    Book  Google Scholar 

  4. Niemyska, W., Baczyński, M., Wąsowicz, S.: Sheffer Stroke Fuzzy Implications. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K.T., Krawczak, M. (eds.) IWIFSGN/EUSFLAT-2017. AISC, vol. 643, pp. 13–24. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-66827-7_2

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Acknowledgment

M. Baczyński and W. Niemyska were supported by the National Science Centre, Poland, under Grant No. 2015/19/B/ST6/03259. P. Helbin has been supported from statutory activity of the Institute of Mathematics, University of Silesia in Katowice. P. Berruezo, S. Massanet and D. Ruiz-Aguilera acknowledge the partial support by the Spanish Grant TIN2016-75404-P, AEI/FEDER, UE.

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Authors and Affiliations

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

    Piotr Helbin & Michał Baczyński

  2. Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Wanda Niemyska

  3. Soft Computing, Image Processing and Aggregation (SCOPIA) Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, 07122, Palma, Spain

    Pedro Berruezo, Sebastia Massanet & Daniel Ruiz-Aguilera

  4. Balearic Islands Health Research Institute (IdISBa), 07010, Palma, Spain

    Pedro Berruezo, Sebastia Massanet & Daniel Ruiz-Aguilera

Authors
  1. Piotr Helbin
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  2. Wanda Niemyska
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  3. Pedro Berruezo
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  4. Sebastia Massanet
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  5. Daniel Ruiz-Aguilera
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  6. Michał Baczyński
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Corresponding author

Correspondence to Michał Baczyński .

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Editors and Affiliations

  1. Częstochowa University of Technology, Częstochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Rafał Scherer

  3. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  4. University of Alberta, Edmonton, AB, Canada

    Witold Pedrycz

  5. AGH University of Science and Technology, Kraków, Poland

    Ryszard Tadeusiewicz

  6. University of Louisville, Louisville, KY, USA

    Jacek M. Zurada

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Helbin, P., Niemyska, W., Berruezo, P., Massanet, S., Ruiz-Aguilera, D., Baczyński, M. (2018). On Fuzzy Sheffer Stroke Operation. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2018. Lecture Notes in Computer Science(), vol 10842. Springer, Cham. https://doi.org/10.1007/978-3-319-91262-2_56

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  • DOI: https://doi.org/10.1007/978-3-319-91262-2_56

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91261-5

  • Online ISBN: 978-3-319-91262-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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