| Title of paper:
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On intuitionistic fuzzy modal operators
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| Author(s):
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| Sinem Yilmaz
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| Mersin University Faculty of Arts and Sciences, Department of Mathematics
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| sinemyilmaz@mersin.edu.tr
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| Gökhan Çuvalcioğlu
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| Mersin University Faculty of Arts and Sciences, Department of Mathematics
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| gcuvalcioglu@mersin.edu.tr
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| Published in:
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"Notes on IFS", Volume 22, 2016, Number 5, pages 27—36
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| Download:
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 PDF (123 Kb, Info)
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| Abstract:
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In 1965, Fuzzy Set Theory was introduced by Zadeh as an extension of crisp sets [10]. K. T. Atanassov defined the concept of Intuitionistic Fuzzy Sets, in 1983 [1]. Some operations and operators on intuitionistic fuzzy sets, like modal operators, level operators, topological operators, etc., was defined by same author [2]. In later times, new operators were defined on IFSs and several properties of these operators were studied by different authors [3, 5, 6, 7, 8, 9]. In this study, we examine some relationships between new modal operators with topological operators.
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| Keywords:
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Intuitionistic fuzzy sets, Intuitionistic fuzzy modal operators, Intuitionistic fuzzy topological operators.
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| AMS Classification:
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03E72, 47S40.
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| References:
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- Atanassov, K.T. (1983) Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, 20–23 June 1983. (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6.
- Atanassov, K.T. (2012) On Intuitionistic Fuzzy Sets Theory, Series "Studies in Fuzziness and Soft Computing", Springer.
- Atanassov, K.T., Çuvalcioğlu, G. & Atanassova V. K. (2014) A new modal operator over intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 20(5), 1–8.
- Atanassov, K.T., Çuvalcioğlu, G., Yılmaz, S., & Atanassova V. K. (2015) Properties of the intuitionistic fuzzy modal operator ⊗α,β,γ,δ, Notes on Intuitionistic Fuzzy Sets, 21(4), 1–5.
- Çuvalcioğlu, G. (2013) On the diagram of one type modal operators on intuitionistic fuzzy sets: last expanding with [math]\displaystyle{ Z^{\omega,\theta}_{\alpha,\beta} }[/math], Iranian Journal of Fuzzy Systems, 10(1), 89–106.
- Çuvalcioğlu, G. (2016) One, two and uni-type operators on IFSs Imprecision and Uncertainty in Information Representation and Processing, Angelov, P., Sotirov, S. (Eds.), Springer International Publishing Switzerland, 55–71.
- Çuvalcioğlu, G. & Yılmaz, S. (2015) On new intuitionistic fuzzy operators: Sα,β and Tα,β Kasmera, 43(2), 317–327.
- Dencheva, K. (2004) Extension of intuitionistic fuzzy modal operators ⊞ and ⊠: Proc.of the Second Int. IEEE Symp. Intelligent systems, Varna, June 22–24, 2004, Vol. 3, 21–22.
- Yılmaz, S. & Bal, A. (2014) Extentsion of intuitionistic fuzzy modal operators diagram with new operators, Notes on Intuitionistic Fuzzy Sets, 20(5), 26–35.
- Zadeh, L.A. (1965) Fuzzy Sets, Information and Control, 8, 338–353.
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