| Title of paper:
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A new modal operator over intuitionistic fuzzy sets
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| Author(s):
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| Krassimir Atanassov
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| Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria
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| krat@bas.bg
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| Gökhan Çuvalcioğlu
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| Department of Mathematics, University of Mersin, Mersin, Türkiye
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| gcuvalcioglu@gmail.com
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| Vassia Atanassova
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| Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria
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| vassia.atanassova@gmail.com
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 20 (2014), Number 5, pages 1–8
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| Download:
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 PDF (152 Kb, File info)
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| Abstract:
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A new operator from modal type is introduced over the intuitionistic fuzzy sets. On one hand, this operator functions by reducing the degree of membership or non-membership, and, on the other hand, by simultaneously summing it with a part of the degree of non-membership or membership, respectively. Some of its properties are studied.
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| Keywords:
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Intuitionistic fuzzy modal operator, Intuitionistic fuzzy operation.
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| AMS Classification:
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03E72.
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| References:
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- Atanassov, K., Intuitionistic Fuzzy Sets: Theory and Applications, Springer, Heidelberg, 1999.
- 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.
- Atanassov, K., The most general form of one type of intuitionistic fuzzy modal operators. Part 2. Proceedings of the Twelfth International Conference on Intuitionistic Fuzzy Sets (J. Kacprzyk and K. Atanassov, Eds), Sofia, 17-18 May 2008, Vol. 1. In: Notes on Intuitionistic Fuzzy Sets, Vol. 14, 2008, No. 1, 27–32.
- Atanassov, K., On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012.
- Atanassov, K., A short remark on intuitionistic fuzzy operators Xa,b,c,d,e,f and xa,b,c,d,e,f, Notes on Intuitionistic Fuzzy Sets, Vol. 19, 2013, No. 1, 54–56.
- Cuvalcıoglu, G., Some properties of [math]\displaystyle{ E_{\alpha,\beta} }[/math] operator. Advanced Studies on Contemporary Mathematics, Vol. 14, 2007, No. 2, 305–310.
- Cuvalcıoglu, G., Expand the model operator diagram with [math]\displaystyle{ Z^{\omega}_{\alpha,\beta} }[/math]. Proceedings of the Jangjeon Math. Society, Vol. 13, 2010, No. 3, 403–412.
- Dencheva, K., Extension of intuitionistic fuzzy modal operators ⊞ and ⊠. Proc. of the Second Int. IEEE Symposium “Intelligent Systems”, Varna, June 22-24 2004, Vol. 3, 21–22.
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