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Issue:On some two-parametric intuitionistic fuzzy implications

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Title of paper: On some two-parametric intuitionistic fuzzy implications
Author(s):
Piotr Dworniczak
Department of Applied Mathematics, University of Economics, al. Niepodległości 10, 60-967 Poznań, Poland
p.dworniczak@ue.poznan.pl
Presented at: 15th ICIFS, Burgas, 11-12 May 2011
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 17 (2011) Number 2, pages 8—16
Download:  PDF (141  Kb, File info)
Abstract: 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.
Keywords: Parametric fuzzy implication, Intuitionistic fuzzy logic.
AMS Classification: 03E72
References:
  1. Atanassov, K. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, Vol. 20, 1986, 87–96.
  2. Atanassov, K. Intuitionistic fuzzy implications and Modus Ponens. Notes on Intuitionistic Fuzzy Sets, Vol. 11, 2005, No. 1, 1–5.
  3. Atanassov, K. On some intuitionistic fuzzy implications. Comptes rendus de l’Academie Bulgare des Sciences, Vol. 59, 2008, No. 1, 19–24.
  4. Atanassov, K. On the intuitionistic fuzzy implications and negations. Studies in Computational Intelligence, Vol. 109, 2008, Springer, Berlin, 381–394.
  5. 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.
  6. 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.
  7. Atanassova, L. A new intuitionistic fuzzy implication. Cybernetics and Information Technologies, Vol. 9, 2009, No. 2, 21–25.
  8. Baczyński, M., B. Jayaram. Fuzzy implications. Springer, Berlin, 2008.
  9. 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.
  10. 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.
  11. Klir, G., B. Yuan. Fuzzy Sets and Fuzzy Logic. Prentice Hall, New Jersey, 1995.
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