| Title of paper:
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The extension of modal operators' diagram with last operators
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| Author(s):
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| Gökhan Çuvalcioğlu
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| Department of Mathematics, University of Mersin, Mersin, Turkey
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| gcuvalcioglu@mersin.edu.tr
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| Presented at:
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17th International Conference on Intuitionistic Fuzzy Sets, 1–2 November 2013, Sofia, Bulgaria
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| Published in:
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"Notes on IFS", Volume 19, 2013, Number 3, pages 56—61
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| Download:
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 PDF (193 Kb, File info)
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| Abstract:
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Intuitionistic Fuzzy Modal Operator was defined by Atanassov, he and several authors defined some modal operators. These operators classified by naming with one type and two type modal operators on intuitionistic fuzzy sets. Indeed, Atanassov’s two operators Xa,b,c,d , ⦾α,β,γ,δ,ε,ζ are both one and two type modal operators. In this paper, we defined four operators which are both one and two type modal operators as Atanassov’s above operators and called them uni-type modal operators.
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| Keywords:
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Diagram of modal operators, Intuitionistic fuzzy operators, Uni-type modal 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., Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, Vol. 20, 1986, 87–96.
- Atanassov, K. T., Intuitionistic Fuzzy Sets, Phiysica-Verlag, Heidelberg, 1999.
- Atanassov, K. T., Remark on Two Operations Over Intuitionistic Fuzzy Sets, Int. J. of Uncertainty, Fuzziness and Knowledge Syst., Vol. 9, 2001, No. 1, 71–75.
- Atanassov, K. T., 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. T., Some properties of the operators from one type of intuitionistic fuzzy modal operators, Advanced Studies on Contemporary Mathematics, Vol. 15, 2007, No. 1, 13–20.
- Atanassov, K. T., The most general form of one type of intuitionistic fuzzy modal operators, Part 2, Notes on Intuitionistic Fuzzy Sets, Vol. 14, 2008, No. 1, 27–32.
- Çuvalcıoğlu, G., Some properties of Eα,β operator, Advanced Studies on Contemporary Mathematics, Vol. 14, 2007, No. 2, 305–310.
- Çuvalcıoğlu, G., 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, Vol. 10, 2013, No. 1, 89–106.
- Dencheva, K., Extension of intuitionistic fuzzy modal operators ⊞ and ☒, Proc. of the Second Int. IEEE Symp. Intelligent Systems, Varna, 22-24 June 2004, Vol. 3, 21–22.
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