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