| Title of paper:
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Modifications of Łukasiewicz’s intuitionistic fuzzy implication
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| Author(s):
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| Alžbeta Michálková
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Faculty of Natural Sciences, Matej Bel University, Tajovského 40, Banská Bystrica, Slovakia
Mathematical Institute, Slovak Academy of Sciences, Ďumbierska 1, Banská Bystrica, Slovakia
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| alzbeta.michalikova@umb.sk
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| Eulalia Szmidt
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Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01 – 447 Warsaw, Poland
Warsaw School of Information Technology, ul. Newelska 6, 01 – 447 Warsaw, Poland
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| szmidt@ibspan.waw.pl
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| Peter Vassilev
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| Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. Georgi Bonchev Str., 1113 Sofia, Bulgaria
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| peter.vassilev@gmail.com
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 3, pages 32–39
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| DOI:
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https://doi.org/10.7546/nifs.2021.27.3.32-39
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| Download:
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 PDF (167 Kb, File info)
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| Abstract:
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In [6], G. Klir and B. Yuan named after J. Łukasiewicz the implication [math]\displaystyle{ p \rightarrow q = min(1, p+q) }[/math]. In a series of papers, 198 different intuitionistic fuzzy implications have been introduced, and their basic properties have been studied. Here we introduce six new implications which are modifications of Łukasiewicz’s intuitionistic fuzzy implication, and we describe and prove some of their properties.
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| Keywords:
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Intuitionistic fuzzy implication, Intuitionistic fuzzy set, Łukasiewicz’s fuzzy implication.
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| AMS Classification:
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03E72.
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| References:
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- Atanassov, K. (2006). On some intuitionistic fuzzy implications. Comptes Rendus de l’Academie bulgare des Sciences, 59(1), 19–24.
- Atanassov, K. (2017). Intuitionistic Fuzzy Logics, Springer, Cham, 2017.
- Atanassov, K., Szmidt, E., & Kacprzyk, J. (2013). On intuitionistic fuzzy pairs. Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13.
- Dworniczak, P., Atanassova, L., & Angelova, N. Modal type of weak intuitionistic fuzzy implications generated by the operation △. Cybernetics and Information Technologies (submitted)
- Feys, R. (1965). Modal Logics. Gauthier-Villars, Paris.
- Klir, G., & Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic. Prentice Hall, New Jersey.
- Mendelson, E. (1964). Introduction to Mathematical Logic, Princeton, NJ: D. Van Nostrand; Fourt Ed. 2001.
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