| Title of paper:
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Automatic verification of properties of intuitionistic fuzzy connectives via Mathematica
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| Author(s):
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| Trifon Trifonov
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| Faculty of Mathematics and Informatics, Sofia University
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| triffon@fmi.uni-sofia.bg
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| Presented at:
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7th IWIFS, Banska Bystrica, 27 September 2011
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| Published in:
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Conference proceedings, "Notes on IFS", Volume 17 (2011) Number 4, pages 11—15
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| Download:
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 PDF (144 Kb, Info)
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| Abstract:
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Intuitionistic fuzzy logic as defined by K. Atanassov [1, 3], is an extension of fuzzy logic, using the more general intuitionistic fuzzy sets as a model. The extension allows for many different definitions of various logical connectives, such as implication and negation, which can be suitable for different needs. This paper suggests a method for automatic verification of properties of intuitionistic fuzzy connectives using the computer algebra system Mathematica [6].
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| Keywords:
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Intuitionistic fuzzy logic, Mathematica, computer algebra, automatic verification
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| AMS Classification:
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03B35, 03B52, 03E72, 68T15, 68W30
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| References:
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- Atanassov, K. (1983) Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulg.).
- Atanassov, K. (1988) Two variants of intuitonistic fuzzy propositional calculus. Preprint IM-MFAIS-5-88, Sofia.
- Atanassov, K. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Physica Verlag, Heidelberg.
- Atanassov, K. (2005) Intuitionistic fuzzy implications and Modus Ponens. Notes on IFS, Vol. 11, No. 1, 1–4.
- Atanassov, K., G. Gargov. (1990) Intuitionistic fuzzy logic. Comptes Rendus de l’Academie bulgare des Sciences, Tome 43, 9–12.
- Wolfram, S. Mathematica: A System for Doing Mathematics by Computer. Addison-Wesley Longman Publishing Co., Inc., 1988, Boston, MA, USA.
- Trifonov, T., K. Atanassov. (2006) On some intuitionistic properties of intuitionistic fuzzy implications and negations. In: Computational Intelligence, Theory and Applications (Reusch B., Ed.), Vol.38, Advances in Soft Computing, Dortmund, Germany. Springer, Berlin, September 2006, 151–158.
- Klir, G., B. Yuan. (1995) Fuzzy Sets and Fuzzy Logic, Prentice Hall, New Jersey.
- Rasiova, H., R. Sikorski. (1963) The Mathematics of Metamathematics, Pol. Acad. of Sci. Warszawa
- Dimitrov, D. (2011) IFSTool – software for intuitionistic fuzzy sets. Issues in IFSs and GNs, Vol. 9, 61–69.
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