| Title of paper:
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The resolution theorems for intuitionistic fuzzy sets with sheet-level sets
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| Author(s):
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| Arif Bal
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| Department of Mathematics, Mersin University, 33016, Mersin Turkey
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| arif.bal.math@gmail.com
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| Gökhan Çuvalcıoğlu
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| Department of Mathematics, Mersin University, 33016, Mersin Turkey
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| gcuvalcioglu@gmail.com
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| Gül Tümen
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| Department of Mathematics, Mersin University, 33016, Mersin Turkey
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| gultumenn@gmail.com
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 25 (2019), Number 2, pages 20–24
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| DOI:
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https://doi.org/10.7546/nifs.2019.25.2.20-24
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| Download:
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 PDF (178 Kb, File info)
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| Abstract:
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In this study, the resolution theorems for IFSs were given by using the α–t sheet level set and strict α–t sheet level set of IFSs. For the second resolution theorem, the definition of strict α–t sheet level set of IFSs was given in this paper. Because of the nature of IFSs, one might give those theorems using fuzzy sets. In this paper, that problem was solved.
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| Keywords:
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Intuitionistic fuzzy sets, IFS Sheet t-level, IFS α–t sheet level and intuitionistic fuzzy t-subset, Resolution theorems.
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| AMS Classification:
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03E72, 03E99
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| References:
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- Atanassov K. T. (1983). Intuitionistic Fuzzy Sets, VII ITKR's Session, Sofia, 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. (1999). Intuitionistic Fuzzy Sets: Theory and Applications, Heidelberg, Springer.
- Çuvalcıoğlu, G., & Yılmaz, S. (2014). Some properties of intuitionistic fuzzy equivalence relations and class trees w.r.t. intuitionistic fuzzy equivalence relations, Adv. Studies Contemp. Math., 24 (4), 77–86.
- Çuvalcıoğlu, G. & Tarsuslu (Yılmaz), S. The block and sheet levels of intuitionistic fuzzy sets, Journal of Universal Mathematics, (under review).
- Çuvalcıoğlu, G., Tarsuslu (Yılmaz), S., & Demirbaş, E. (2019). Sheet level sets and representation theorem for intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 25 (2), 15–19.
- Maheswari, A., Karthikeyan S. & Palanivelrajan, M. (2012). Characterization of level sets of intuitionistic L-fuzzy semi filter of lattices, Notes on Intuitionistic Fuzzy Sets, 18 (2), 21–25.
- Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, 338–353.
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