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Issue:On an operator, mapping intuitionistic fuzzy sets into fuzzy sets

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Title of paper: On an operator, mapping intuitionistic fuzzy sets into fuzzy sets
Author(s):
Peter Vassilev
Bioinformatics and Mathematical Modelling Department, IBPhBME - Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., block 105, Sofia 1113, Bulgaria
peter.vassilev@gmail.com
Presented at: 9th International Workshop on Intuitionistic Fuzzy Sets, 8 October 2013, Banská Bystrica, Slovakia
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 19, 2013, Number 2, pages 21—24
Download:  PDF (124  Kb, File info)
Abstract: In the present paper a possible way for defining a hesitancy-dependent operator mapping the class of intuitionistic fuzzy sets to the class of fuzzy sets is proposed. It is proved that the so-defined operator preserves ordering (in the sense of inclusion.
Keywords: Operator, Fuzzy set, Intuitionistic fuzzy set, hesitancy function.
AMS Classification: 03E72
References:
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  2. Atanassov, K. Intuitionistic Fuzzy Sets: Theory and Applications, Springer Physica-Verlag, Heidelberg, 1999.
  3. Atanassov, K. On Intuitionistic Fuzzy Sets Theory, Springer Physica-Verlag, Berlin, 2012.
  4. Ban, A., J. Kacprzyk, K. Atanassov. On de-I-fuzzification of intuitionistic fuzzy sets. Comptes Rendus de l’Academie bulgare des Sciences, Vol. 61, 2008, No. 12, 1535-1540.
  5. Grzegorzewski, P. E. Mrowka. Some notes on (Atanassov’s) intuitionistic fuzzy sets. Fuzzy Sets and Systems, Vol. 156, 2005, 492–495.
  6. Kaufmann A. Theory of expertons and fuzzy logic, Fuzzy Sets and Systems, Vol. 28, 1988, No. 3, 295–304.
  7. Klir, G, B. Yuan. Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hail, New Jersey, 1995.
  8. Zadeh, L. Fuzzy sets. Information and Control, Vol. 8, 1965, 338–353.
  9. Zadeh, L. The concept of a linguistic variable and its application to approximate reasoning, American Elsevier Publ. Co., New York, 1973.
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