| Title of paper:
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Intuitionistic fuzzy sets and interval valued fuzzy sets
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| Author(s):
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| Krassimir Atanassov
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| CLBME-Bulgarian Academy of Sciences, P.O. Box 12, Sofia-1113, Bulgaria
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| krat@bas.bg
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| Presented at:
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First International Workshop on Intuitionistic Fuzzy Sets, Generalized Nets and Knowledge Engineering. London, 6-7 September 2006
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| Published in:
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Conference proceedings, pages 1-7
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| Download:
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 PDF (143 Kb, File info)
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| Abstract:
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Some relationships and differences between two extensions of the fuzzy sets — intuitionistic fuzzy sets and interval valued fuzzy sets are discussed.
The advent of the concept of "fuzzy set" introduced by Lotfi Zadeh in 1965 is one of the most important events in the mathematics of the second half of twentieth century. It is not only an abstract mathematical object, extending J. Lukasiewicz's idea for 3- and n-valued logics, but is also during the last 30 years one of the most used mathematical concept in practice. For these reasons fuzzy sets are an object of different extensions and modifications. Two of them are the concepts of Intuitionistic Fuzzy Sets (IFSs) and Interval Valued Fuzzy Sets (IVFSs). Here we shall discuss some relationships and differences between both types of sets.
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| Keywords:
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Intuitionistic fuzzy sets, Interval-valued fuzzy sets, Extensions of fuzzy sets
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| References:
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- Atanassov K., Temporal intuitionistic fuzzy sets. Comptes Rendus de l'Academie bulgare des Sciences, Tome 44, 1991, No. 7, 5-7.
- Atanassov K., Intuitionistic Fuzzy Sets, Springer Physica-Verlag, Berlin, 1999.
- Atanassov K., G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 31, 1989, No. 3, 343-349.
- Atanassov K., V. Kreinovich, Intuitionistic fuzzy interpretation of interval data, Notes on Intuitionistic Fuzzy Sets, Vol. 5 (1999), No. 1, 1-8.
- Szmidt, E. Applications of Intuitionistic Fuzzy Sets in Decision Making. D.Sc. dissertation, Technical University, Sofia, 2000.
- Szmidt, E., J. Baldwin. Entropy for intuitionistic fuzzy set theory and mass assignment theory. Proceedings of the Eight International Conference on Intuitionistic Fuzzy Sets (J. Kacprzyk and K. Atanassov, Eds.), Sofia, 20-21 June 2004, Vol. 1, Notes on Intuitionistic Fuzzy Sets, Vol. 10 (2004), No. 3, p 15-28.
- Szmidt, S., J. Kacprzyk. Concept of distances and entropy for intuitionistic fuzzy sets and their applications in group decision making. Notes on Intuitionistic Fuzzy Sets, Vol. 8, 2002, No. 3, 11-25.
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