| Title of paper:
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On Zadeh's intuitionistic fuzzy disjunction and conjunction
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| Author(s):
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| Krassimir Atanassov
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| Dept. of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria
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| krat@bas.bg
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| Published in:
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"Notes on Intuitionistic Fuzzy Sets", Volume 17 (2010) Number 1, pages 1—4
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| Download:
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 PDF (96 Kb, File info)
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| Abstract:
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During the last ten years a lot of operations were defined over intuitionistic fuzzy sets (IFSs; see [3]). Here, we will discuss three operations, generated by Zadeh's implication, introduced in fuzzy set theory (see, e.g., [8]). Its IFS-analogues was introduced in [5, 6] and here, on its basis, we will construct Zadeh's conjunction and disjunction.
In [8] 10 different fuzzy implications are discussed. Having in mind that in the classical logic the equality
x V y = ¬x → y,
where x and y are logical variables, V - disjunction, → - implication and ¬ - negation, we see that for any implication we can construct a disjunction and after this, using De Morgan's laws - a conjunction (or opposite).
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| References:
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- Atanassov, K. Two variants of intuitionistic fuzzy propositional calculus. Preprint IM-MFAIS-5-88, Sofia, 1988.
- Atanassov K., Two variants of intuitionistic fuzzy modal logic. Preprint IM-MFAIS-3-89, Sofia, 1989.
- Atanassov, K. Intuitionistic Fuzzy Sets, Springer Physica-Verlag, Heidelberg, 1999.
- Atanassov, K. Remarks on the conjunctions, disjunctions and implications of the intuitionistic fuzzy logic Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 9, 2001, No. 1, 55-65.
- 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, Tome 59, 2006, No. 1, 19-24.
- Feys, R., Modal logics, Gauthier, Paris, 1965.
- Klir, G., B. Yuan, Fuzzy Sets and Fuzzy Logic. Prentice Hall, New Jersey, 1995.
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