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Issue:Towards combining two kinds of intuitionistic fuzzy sets

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Title of paper: New measures of entropy for intuitionistic fuzzy sets
Author(s):
Krassimir Atanassov
CLBME - Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia-1113, Bulgaria
krat@bas.bg
Trifon Trifonov
CLBME - Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia-1113, Bulgaria
trifonov@clbme.bas.bg
Presented at: 9th ICIFS, Sofia, 7-8 May 2005
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 11 (2005) Number 2, pages 1—11
Download:  PDF (173  Kb, File info)
Abstract: In this paper the authors discuss how intuitionistic fuzzy sets as defined by Atanassov in [1] can be combined with a construction by Takeuti and Titani ([12]), given by its authors the same name. The resulting object, has the semantics of the former, while satisfying the axioms of the latter. Correctness of the construction is proved in the axiomatic system presented in [12].
Keywords: Intuitionistic fuzzy sets
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 Bulg.).
  2. Atanassov K., Two variants of intuitionistic fuzzy propositional calculus. Preprint IM-MFAIS-5-88, Sofia, 1988.
  3. Atanassov K., Remark on intuitionistic fuzzy logic and intuitionistic logic, Mathware, Vol. 2, No. 2, 1995, 151-156.
  4. Atanassov, K. Intuitionistic Fuzzy Sets. Springer-Physica Verlag, Heidelberg, 1999.
  5. Atanassov, K., Elements of intuitionistic fuzzy logics. Part II: Intuitionistic fuzzy modal logics. Advanced Studies on Contemporary Mathematics, Vol. 5, 2002, No. 1, 1-13.
  6. Atanassov, K., Intuitionistic fuzzy implications and Modus Ponens. Notes on IFS, Vol. 11 (2005), No. 1, 1-4.
  7. Atanassov, K., New intuitionistic fuzzy negations (in preparation).
  8. Atanassov K., Gargov G., Intuitionistic fuzzy logic. Comptes Rendus de l'Academie bulgare des Sciences, Tome 43, 1990, No.
  9. Atanassov, K., G. Gargov. Elements of intuitionistic fuzzy logic. I. Fuzzy sets and Systems Vol. 95, 1998, No. 1, 39-52.
  10. Deschrijver G., E. Kerre, On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems, Vol. 133 (2003), No. 2, 227-235.
  11. Nikolova M., N. Nikolov, C. Cornelis, G. Deschrijver, Survey of the research on intuitionistic fuzzy sets. Advanced Studies in Contemporary Mathematics, Vol. 4, 2002, No. 2, 127-157.
  12. Takeuti G., Titani S. Intuitionistic fuzzy logic and intuitionistic fuzzy set theory. The Journal of Symbolic Logic, Vol. 49, No. 3, Sept. 1984, 851-866.
Citations:
  1. Atanassov K., On some intuitionistic fuzzy implications, Comptes Rendus de l'Academie bulgare des Sciences, Tome 59, No 1, 2006, pages 19-24

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