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Issue:Theorem for equivalence of the two most general intuitionistic fuzzy modal operators

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Title of paper: Theorem for equivalence of the two most general intuitionistic fuzzy modal operators
Author(s):
Krassimir Atanassov
CLBME - Bulgarian Academy of Sciences, P.O.Box 12, Sofia-1113, Bulgaria
krat@bas.bg
Presented at: 13th ICIFS, Sofia, 9-10 May 2009
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 15 (2009) Number 1, pages 26—31
Download:  PDF (77  Kb, File info)
Abstract: In a series of research the two types of modal operators, defined over the intuitionistic fuzzy sets (IFSs) were generalized to two operators. Here, we will prove that they coincide.


References:
  1. Atanassov K. Intuitionistic fuzzy sets, VII ITKR's Session, Sofia, June 1983 (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian).
  2. Atanassov K., Some operators on intuitionistic fuzzy sets, Proceedings of the First International Conference on Intuitionistic Fuzzy Sets (J. Kacprzyk and K. Atanassov Eds.), Sofia, Oct 18-19, 1997; Notes on Intuitionistic Fuzzy Sets, Vol. 3 (1997), No. 4, 28-33.
  3. Atanassov K., Intuitionistic Fuzzy Sets, Springer Physica-Verlag, Berlin, 1999.
  4. Atanassov K. On one type of intuitionistic fuzzy modal operators. Notes on Intuitionistic Fuzzy Sets, Vol. 11, 2005, No. 5, 24-28.
  5. Atanassov K. The most general form of one type of intuitionistic fuzzy modal operators. Notes on Intuitionistic Fuzzy Sets, Vol. 12, 2006, No. 2, 36-38.
  6. Atanassov K. Some properties of the operators from one type of intuitionistic fuzzy modal operators. Advanced Studies on Contemporary Mathematics, Vol. 15, 2007, No. 1, 13-20.
  7. Atanassov K. The most general form of one type of intuitionistic fuzzy modal operators. Part 2. Notes on Intuitionistic Fuzzy Sets, Vol. 13, 2007, No. 1, 27-32.
  8. Cuvalcioglu, G. Some properties of Eα,β operator. Advanced Studies on Contemporary Mathematics, Vol. 14, 2007, No. 2, 305-310.
  9. Dencheva K. Extension of intuitionistic fuzzy modal operators ⊞ and ⊠. Proceedings of the Second Int. IEEE Symposium: Intelligent Systems, Varna, June 22-24, 2004, Vol. 3, 21-22.
  10. Feis, Modal Logics, Gauthier-Villars, Paris, 1965.
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