| Title of paper:
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Some algebraic 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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| Gökhan Çuvalcioğlu
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| Department of Mathematics, University of Mersin, Turkey
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| gcuvalcioglu@gmail.com
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| Arif Bal
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| Department of Mathematics, University of Mersin, Turkey
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| arif.bal.math@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 6—18
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| Download:
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 PDF (187 Kb, File info)
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| Abstract:
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Intuitionistic fuzzy sets were introduced by Atanassov in 1983 [1]. He defined Intuitionistic Fuzzy Modal Operators on IFSs. Intuitionistic fuzzy modal operators were separated in three types called one-two-uni type modal operators on Intuitionistic Fuzzy Sets with the help of some authors’ studies [3, 5]. A study named Matrix Representation of the Second Type of Intuitionistic Fuzzy Modal Operators introduced in [4]. In this study, our purpose is to examine some new algebraic properties of matrix representation sets of Intuitionistic Fuzzy Modal Operators which is a monoid with the matrix product and give the concept of generator in this algebraic structure.
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| Keywords:
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Intuitionisic fuzzy sets, Intuitionistic fuzzy modal operators, Matrix representation of IFMOs on IFSs, Algebraic properties of matrix representation of IFMOs on IFSs.
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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., 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.
- Hungerford, T. W. Algebra, Springer-Verlag NY Inc, 1974
- L. A. Zadeh, Fuzzy sets, Information and Control, 8 , 1965, 338-353.
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| Citations:
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