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Issue:Some modal operators with intuitionistic fuzzy sets

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Title of paper: Some modal operators with intuitionistic fuzzy sets
Author(s):
Sinem Tarsuslu
Department of Mathematics, Faculty of Arts and Sciences, Mersin University, Mersin, Turkey
sinemnyilmaz@gmail.com
Mehmet Çitil
Department of Mathematics, Faculty of Arts and Sciences, Kahramanmaras¸ Sutcu Imam University, Kahramanmaras, Turkey
citil@ksu.edu.tr
Emine Demirbaş
Department of Mathematics, Faculty of Arts and Sciences, Mersin University, Mersin, Turkey
eminesdemirbas@gmail.com
Mehmet Aydın
Department of Mathematics, Faculty of Arts and Sciences, Mersin University, Mersin, Turkey
mathmetaydin@gmail.com
Published in: "Notes on IFS", Volume 23, 2017, Number 5, pages 20—28
Download:  PDF (172 Kb  Kb, File info)
Abstract: Intuitionistic fuzzy modal operators has been studied by many researchers. The characteristics of modal operators have been examined and their applications in different fields have been studied. Atanassov introduced new modal operators with intuitionistic fuzzy sets and he examined some properties of these generalized modal operators. In this paper, we defined new modal operators over the intuitionistic fuzzy sets which undefined over intuitionistic fuzzy sets by Atanasov and we obtained some characteristics of them.
Keywords: Intuitionistic fuzzy sets, Intuitionistic fuzzy modal operators, Generalized intuitionistic fuzzy modal operators.
AMS Classification: 03E72, 47S40.
References:
  1. Atanassov, K.T. (1983) Intuitionistic Fuzzy Sets, VII ITKR 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.
  2. Atanassov, K.T. (1999) Intuitionistic Fuzzy Sets, Springer- Physica Verlag, Heidelberg.
  3. Atanassov, K. T. (2004) On the modal operators defined over the intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 10(1), 7–12.
  4. Atanassov, K. T. (2012) On Intuitionistic Fuzzy Sets Theory, Springer, Heidelberg.
  5. Atanassov, K. T., Cuvalcıoglu, G., & Atanassova, V. (2014) A new modal operator over intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, 20(5), 1–8.
  6. Cuvalcıoglu, G. (2007) Some Properties of Eα,β operator, Advanced Studies on Contemporary Mathematics, 14(2), 305–310.
  7. Cuvalcıoglu, G. (2013) On the diagram of One Type Modal Operators on Intuitionistic Fuzzy Sets: Last Expanding with Zα,βω,θ, Iranian Journal of Fuzzy Systems, 10(1), 89–106.
  8. Cuvalcıoglu, G. (2016) One, two and uni-type operators on IFSs, Studies in Fuzziness and Soft Computing, 332, 55–71.
  9. Dencheva, K. (2004) Extension of intuitionistic fuzzy modal operators ⊞ and ⊠, Proc.of the Second Int. IEEE Symp. Intelligent systems, 3, 21–22.
  10. Yılmaz, S., & Çuvalcioğlu, G., Intuitionistic fuzzy modal operators: Sα,β and Tα,β. 28th National Mathematical Symposium, Antalya, 07-09 September 2015.
  11. Yılmaz, S., & Bal, A. (2014) Extension of intuitionistic fuzzy modal operators diagram with new operators, Notes on Intuitionistic Fuzzy Sets, 20(5), 26–35.
  12. Zadeh, L. A. (1965) Fuzzy Sets, Information and Control, 8, 338–353.
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