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Issue:On intuitionistic fuzzy implications, negations and the law (¬A ⊃ ¬B) ⊃ ((¬A ⊃ ¬¬B) ⊃ ¬¬A)

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Title of paper: On intuitionistic fuzzy implications, negations and the law (¬A ⊃ ¬B) ⊃ ((¬A ⊃ ¬¬B) ⊃ ¬¬A)
Author(s):
Krassimir Atanassov
Bioinformatics and Mathematical Modelling Department, IBPhBME - Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., block 105, Sofia 1113, Bulgaria
krat@bas.bg
Presented at: 9th International Workshop on Intuitionistic Fuzzy Sets, 8 October 2013, Banská Bystrica, Slovakia
Published in: "Notes on IFS", Volume 19, 2013, Number 2, pages 10-20
Download:  PDF (124  Kb, Info)
Abstract: In a series of papers,the intuitionistic fuzzy logis is extended with different negations and imnplications. Here, all implications and generated by them negations, that satisfy the laws (¬A⊃¬B)⊃((¬A⊃¬¬B)⊃¬¬A) and (¬A⊃¬B)⊃((¬A⊃B)⊃A) are described.
Keywords: Implication, Intuitionistic fuzzy logic, Negation
AMS Classification: 03E72
References:
  1. Atanassov, K. Two variants of intuitonistic fuzzy propositional calculus.Preprint IM-MFAIS-5-88, Sofia, 1988.
  2. Atanassov, K. Intuitionistic Fuzzy Sets: Theory and Applications, Springer, Heidelberg, 1999.
  3. Atanassov, K. On intuitionistic fuzzy negations and De Morgan laws. Proc. of Eleventh International Conf. IPMU 2006, Paris, July 2–7, 2006, 2399–2404.
  4. Atanassov, K. A new intuitionistic fuzzy implication from a modal type. Advanced Studies in Contemporary Mathematics, Vol. 12, 2006, No. 1, 117–122.
  5. Atanassov, K. On some intuitionistic fuzzy implications. Comptes Rendus de l’Academie bulgare des Sciences, Vol. 59, 2006, No. 1, 19–24.
  6. Atanassov, K. On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012.
  7. Atanassova, L. A new intuitionistic fuzzy implication. Cybernetics and Information Technologies, Vol. 9, 2009, No. 2, 21–25.
  8. Atanassova, L. On two modifications of the intuitionistic fuzzy implication →@. Notes on Intuitionistic Fuzzy Sets, Vol. 18, 2012, No. 2, 26–30.
  9. Atanassova, L. On the modal form of the intuitionistic fuzzy implications →′@ and →′′@. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, Vol. 10, 5–11.
  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. Dworniczak, P. On one class of intuitionistic fuzzy implications. Cybernetics and Information Technologies, Vol. 10, 2010, No. 4, 13–21.
  12. Dworniczak, P. On some two-parametric intuitionistic fuzzy implication. Notes on Intuitionistic Fuzzy Sets, Vol. 17, 2011, No. 2, 8–16
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