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Issue:Intuitionistic fuzzy action of a group on a set

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Title of paper: Intuitionistic fuzzy action of a group on a set
Author(s):
Sinem Tarsuslu
Mersin University, Faculty of Arts and Sciences, Department of Mathematics, Mersin, Turkey
sinemnyilmaz@gmail.com
Ali Tarsuslu
Private Science Academy Children’s Club, Mersin, Turkey
alitarsuslu@gmail.com
Mehmet Çitil
Kahramanmaras, Sütcü Imam University, Faculty of Arts and Sciences, Department of Mathematics, Kahramanmaras, Turkey
mehmet.citil4600@gmail.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 2, pages 18–24
DOI: https://doi.org/10.7546/nifs.2018.24.2.18-24
Download:  PDF (174 Kb  Kb, File info)
Abstract: Intuitionistic fuzzy set theory was introduced by Atanassov as an extension of fuzzy sets [1]. The algebraic structures like groups, rings, modules, etc. were generalized to intuitionistic fuzzy sets by different authors. Some properties of them were studied [4, 9, 11, 14, 15]. In this study, we generalized the action of a group on a set to intuitionistic fuzzy action. We obtained some basic results.
Keywords: Intuitionistic fuzzy sets, Intuitionistic fuzzy algebraic structures, Intuitionistic fuzzy actions.
AMS Classification: 03E72, 47S40
References:
  1. Atanassov, K. T. (1983) Intuitionistic Fuzzy Sets, VII ITKR 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.
  2. Atanassov, K. T. (1999) Intuitionistic Fuzzy Sets, Spinger, Heidelberg.
  3. Atanassov, K. T., C¸ uvalcıo˘glu G., & Atanassova, V. (2014) A new modal operator over intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 20(5), 1–8.
  4. Biswas, R. (1989) Intuitionistic fuzzy subgroups, Mathematical Forum, Vol. X, 37–46.
  5. Boixader, D., & Recasens, J. (2018) Fuzzy Actions, Fuzzy Sets and Systems, 339, 17–30.
  6. Burillo, P., & Bustince, H. (1995) Intuitionistic fuzzy relations (Part I) Mathware & Soft Computing, 2, 5–38.
  7. Bustince, H., & Burillo, P. (1996) Structures on intuitionistic fuzzy relations, Fuzzy Sets and Systems, 78, 293–303.
  8. Cuvalcıoglu, G. (2010) Expand the modal operator diagram with [math]\displaystyle{ Z_{\alpha,\beta}^{\omega} }[/math], Proc. Jangjeon Math. Soc, 13 (3), 403–412.
  9. Cuvalcıoglu, G. & Tarsuslu (Yılmaz), S. (2017) Universal algebra in intuitionistic fuzzy set theory, Notes on Intuitionistic Fuzzy Sets, 23(1), 1–5.
  10. Hungerford, T. W. (1974) Algebra, Springer, Verlag, New York Inc.
  11. Hur, K., Jang Y. & Kang H. W. (2003) Intuitionistic fuzzy Subgroupoid, Int. Jour. of Fuzzy Logic and Int. Sys., 3(1), 72–77.
  12. Yılmaz, S., Cuvalcıoglu, G. (2014) On level operators for temporal intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 20(2), 6–15.
  13. Hur, K., Jang, S. Y. & Ahn, Y. S. (2005) Intuitionistic fuzzy equivalence relations, Honam Math. J. 27(2), 163–181.
  14. Yılmaz, S., Cuvalcıoglu, G. (2016). On Study of Some Intuitionistic Fuzzy Operators for Intuitionistic Fuzzy Algebraic Structures, Journal of Fuzzy Set Valued Analysis, 2016(3), 317–325.
  15. Yan, L., (2008) Intuitionistic Fuzzy Ring and Its Homomorphism Image, Int. Seminar on FBM Inf. Eng., 75–77.
  16. Zadeh, L.A. (1965) Fuzzy Sets, Information and Control, 8, 338–353.
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