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Issue:Automatic verification of properties of intuitionistic fuzzy connectives via Mathematica

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Title of paper: Automatic verification of properties of intuitionistic fuzzy connectives via Mathematica
Author(s):
Trifon Trifonov
Faculty of Mathematics and Informatics, Sofia University
triffon@fmi.uni-sofia.bg
Presented at: 7th IWIFS, Banska Bystrica, 27 September 2011
Published in: Conference proceedings, "Notes on IFS", Volume 17 (2011) Number 4, pages 11—15
Download:  PDF (144  Kb, File info)
Abstract: 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].
Keywords: Intuitionistic fuzzy logic, Mathematica, computer algebra, automatic verification
AMS Classification: 03B35, 03B52, 03E72, 68T15, 68W30
References:
  1. 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.).
  2. Atanassov, K. (1988) Two variants of intuitonistic fuzzy propositional calculus. Preprint IM-MFAIS-5-88, Sofia.
  3. Atanassov, K. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Physica Verlag, Heidelberg.
  4. Atanassov, K. (2005) Intuitionistic fuzzy implications and Modus Ponens. Notes on IFS, Vol. 11, No. 1, 1–4.
  5. Atanassov, K., G. Gargov. (1990) Intuitionistic fuzzy logic. Comptes Rendus de l’Academie bulgare des Sciences, Tome 43, 9–12.
  6. Wolfram, S. Mathematica: A System for Doing Mathematics by Computer. Addison-Wesley Longman Publishing Co., Inc., 1988, Boston, MA, USA.
  7. 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.
  8. Klir, G., B. Yuan. (1995) Fuzzy Sets and Fuzzy Logic, Prentice Hall, New Jersey.
  9. Rasiova, H., R. Sikorski. (1963) The Mathematics of Metamathematics, Pol. Acad. of Sci. Warszawa
  10. Dimitrov, D. (2011) IFSTool – software for intuitionistic fuzzy sets. Issues in IFSs and GNs, Vol. 9, 61–69.
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