| Title of paper:
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Some properties of the matrix representation of intuitionistic fuzzy modal operators
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| Author(s):
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| Sinem Yılmaz
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| Department of Mathematics, University of Mersin, Turkey
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| sinemyilmaz@gmail.com
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| Mehmet Çitil
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| Department of Mathematics,, University of Sütçü İmam, K. Maraş, Turkey
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| citil@ksu.edu.tr
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| Gökhan Çuvalcioğlu
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| Department of Mathematics, University of Mersin, Turkey
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| gcuvalcioglu@gmail.com
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| Presented at:
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19th International Conference on Intuitionistic Fuzzy Sets, 4–6 June 2015, Burgas, Bulgaria
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| Published in:
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"Notes on IFS", Volume 21, 2015, Number 2, pages 19—24
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| Download:
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 PDF (200 Kb, Info)
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| Abstract:
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In 1965, Fuzzy Set Theory was defined by L. Zadeh as an extension of crisp sets [2]. K. T. Atanassov generalized fuzzy sets in to Intuitionistic Fuzzy Sets in 1983[2]. Intuitionistic Fuzzy Modal Operator was firstly defined in [2] and the other operators were defined by different autors. Some properties of them have studied until now. Matrix representation of Intuitionistic Fuzzy Modal Operators were defined and some algebraic properties were given in [2]. In this study, we examined some properties of these matrix representations and we obtained some relationships between them.
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| Keywords:
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Intuitionistic fuzzy sets, Intuitionistic fuzzy modal operators, Matrix representation of IFS operators.
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| AMS Classification:
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03E72, 47S40.
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| References:
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- Atanassov, K., Intuitionistic fuzzy sets, Proc. of VII ITKR’s Session, Sofia (deposed June 1983, in Bulgarian)
- Atanassov, K., Intuitionistic Fuzzy Sets, Springer, Heidelberg, 1999.
- Çuvalcioğlu, G., On the Diagram of One Type Modal Operatorss on Intuitionistic Fuzzy Sets: Last Expanding with [math]\displaystyle{ Z^{\omega,\theta}_{\alpha,\beta} }[/math] , Iranian J. of Fuzzy Systems, 10(1), 2013, 89–106.
- Çuvalcıoğlu, G. The Extension of Modal Operators' Diagram with Last Operators, Notes on Intuitionistic Fuzzy Sets, 19(3), 2013, 56–61.
- Çuvalcıoğlu, G., S. Yılmaz and K. Atanassov. Matrix representation of the second type of intuitionistic fuzzy modal operators, Notes on Intuitionistic Fuzzy Sets, 20(5), 2014, 9–16.
- 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.
- L. A. Zadeh, Fuzzy sets, Information and Control, 8 , 1965, 338-353.
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