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# Issue:On level operators for temporal intuitionistic fuzzy sets

 shortcut http://ifigenia.org/wiki/issue:nifs/20/2/6-15
Title of paper: On level operators for temporal intuitionistic fuzzy sets
Author(s):
 Sinem Yılmaz Department of Mathematics, Faculty of Arts and Sciences Mersin University, Mersin, Turkey sinemyilmaz@mersin.edu.tr Gökhan Çuvalcioğlu Department of Mathematics, Faculty of Arts and Sciences Mersin University, Mersin, Turkey gcuvalcioglu@mersin.edu.tr
Presented at: 18th International Conference on Intuitionistic Fuzzy Sets, 10–11 May 2014, Sofia, Bulgaria
Published in: "Notes on IFS", Volume 20, 2014, Number 2, pages 6—15
Abstract: In 1965, Fuzzy Set Theory was defined by Zadeh as an extension of crisp sets, [8]. K. T. Atanassov generalized fuzzy sets in to Intuitionistic Fuzzy Sets in 1983, [1]. He defined some operations and operators on intuitionistic fuzzy sets, like modal operators, level operators etc. In 1991, Atanassov introduced Temporal Intuitionistic Fuzzy Sets. Temporal intuitionistic fuzzy set is an extension of intuitionistic fuzzy set by “time-moments”, [2]. After this extension author shows that all operations and operators on the intuitionistic fuzzy sets can be defined for the temporal intuitionistic fuzzy sets. In 2009, Parvathi and Geetha defined some level operators, max-min implication operators and $\displaystyle{ P_{\alpha,\beta} }$, $\displaystyle{ Q_{\alpha,\beta} }$ operators on temporal intuitionistic fuzzy sets, [7]. In this study we will introduce $\displaystyle{ N_B(A) }$ and $\displaystyle{ N^*_B (A) }$ operators on temporal intuitionistic fuzzy sets with extension to new universal and we will examine some properties of these operators.
Keywords: Intuitionistic fuzzy sets, Temporal intuitionistic fuzzy sets, Level operators.
AMS Classification: 03E72, 47S40.
References:
1. Atanassov, K. T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 20, 1986, 87–96.
2. Atanassov, K. T., Intuitionistic fuzzy sets, Proc. of VII ITKR’s Session, Sofia, June 1983 (in Bulgarian).
3. Atanassov, K. T., On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012, 260–264.
4. Atanassov, K. T., Temporal intuitionistic fuzzy sets, Comptes Rendus de l’Academie Bulgare, Vol. 7, 1991, 5–7.
5. Çuvalcioğlu, G., S. Yılmaz, Extension of intuitionistic fuzzy sets to new universal, Journal of Fuzzy Set Valued Analysis (in press).
6. Parvathi, R., S. P. Geetha, A note on properties of temporal intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, Vol.15, 2009, No. 1, 42–48.
7. Riečan, B.., K. Atanassov, On intuitionistic fuzzy level operators, Notes on Intuitionistic Fuzzy Sets, Vol. 16, 2010, No. 3, 42–44.
8. Zadeh. L.A., Fuzzy sets, Information and Control, Vol. 8, 1965, 338–353.
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