Title of paper:
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On some two-parametric intuitionistic fuzzy implications
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Author(s):
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Piotr Dworniczak
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Department of Applied Mathematics, University of Economics, al. Niepodległości 10, 60-967 Poznań, Poland
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p.dworniczak@ue.poznan.pl
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Presented at:
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15th ICIFS, Burgas, 11-12 May 2011
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Published in:
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Conference proceedings, "Notes on IFS", Volume 17 (2011) Number 2, pages 8—16
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Download:
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PDF (141 Kb, File info)
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Abstract:
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In this paper a new class of two-parametric intuitionistic fuzzy implications is introduced. Fulfillment of some axioms and properties, together with Modus Ponens and Modus Tollens inference rules are investigated. Negation induced by implication is presented.
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Keywords:
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Parametric fuzzy implication, Intuitionistic fuzzy logic.
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AMS Classification:
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03E72
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References:
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- Atanassov, K. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, Vol. 20, 1986, 87–96.
- Atanassov, K. Intuitionistic fuzzy implications and Modus Ponens. Notes on Intuitionistic Fuzzy Sets, Vol. 11, 2005, No. 1, 1–5.
- Atanassov, K. On some intuitionistic fuzzy implications. Comptes rendus de l’Academie Bulgare des Sciences, Vol. 59, 2008, No. 1, 19–24.
- Atanassov, K. On the intuitionistic fuzzy implications and negations. Studies in Computational Intelligence, Vol. 109, 2008, Springer, Berlin, 381–394.
- Atanassov, K. On the intuitionistic fuzzy implications and negations. In: 35 Years of Fuzzy Set Theory. Studies in Fuzziness and Soft Computing 261, Springer, Berlin, 2010, 19–38.
- Atanassov, K., S. Stoeva. Intuitionistic fuzzy sets. In: Albrycht J., H. Wiśniewski (Eds) Proc. of the Polish Symposium on Interval & Fuzzy Mathematics, Poznań, 1985, 23–26.
- Atanassova, L. A new intuitionistic fuzzy implication. Cybernetics and Information Technologies, Vol. 9, 2009, No. 2, 21–25.
- Baczyński, M., B. Jayaram. Fuzzy implications. Springer, Berlin, 2008.
- Czogała, E., J. Łęski. On equivalence of approximate reasoning results using different interpretations of fuzzy if-then rules. Fuzzy Sets and Systems, Vol. 117, 2001, 279–296.
- Dworniczak, P. Some remarks about the L. Atanassova’s paper A new intuitionistic fuzzy implication. Cybernetics and Information Technologies, Vol. 10, 2010, No. 3, 3–9.
- Klir, G., B. Yuan. Fuzzy Sets and Fuzzy Logic. Prentice Hall, New Jersey, 1995.
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