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Issue:A study on extended intuitionistic fuzzy modal operators

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Title of paper: A study on extended intuitionistic fuzzy modal operators
Author(s):
Sinem Tarsuslu (Yılmaz)     0000-0001-9192-7001
Department of Natural and Mathematical Sciences, Faculty of Engineering, Tarsus University, 33400, Tarsus, Türkiye
sinemtarsuslu@tarsus.edu.tr
Gökhan Çuvalcıoğlu     0000-0001-5451-3336
Department of Mathematics, University of Mersin, Mersin, Türkiye
gcuvalcioglu@gmail.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 4, pages 441–447
DOI: https://doi.org/10.7546/nifs.2025.31.4.441-447
Download:  PDF (174  Kb, File info)
Abstract: In this study, extended modal operators [math]\displaystyle{ L_{B}^{D}\left( A\right) }[/math] and [math]\displaystyle{ K_{B}^{D}\left( A\right) }[/math] are presented. The relationships between the newly defined operators and the previously introduced [math]\displaystyle{ T_{B}\left( A\right) }[/math] and [math]\displaystyle{ S_{B}\left( A\right) }[/math] operators with the Necessity and Possibility operators have been examined, and moreover, their algebraic properties regarding inclusion and complement have also been studied.
Keywords: Intuitionistic fuzzy sets, Extended modal operators.
AMS Classification: 03E72.
References:
  1. Atanassov K. T. Intuitionistic fuzzy sets. In: 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 in International Journal of Bioautomation, 20(S1), 2016, S1–S6.
  2. Atanassov, K. T. (2003). A new intuitionistic fuzzy modal operator. Notes on Intuitionistic Fuzzy Sets, 9(2), 56–60.
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  5. Atanassov, K. (2025). A new intuitionistic fuzzy extended modal operator. Notes on Intuitionistic Fuzzy Sets, 31(1), 9–14.
  6. Bhattacharya, J. (2023). Some new results on intuitionistic fuzzy operators. Notes on Intuitionistic Fuzzy Sets, 29(3), 247–260.
  7. Çuvalcıoğlu, G. (2016). New tools based on intuitionistic fuzzy sets and generalized nets (pp. 55–71). Springer.
  8. Çuvalcıoğlu, G., & Tarsuslu (Yılmaz), S. (2017). New properties of [math]\displaystyle{ S_{\alpha,\beta} }[/math] and [math]\displaystyle{ T_{\alpha,\beta} }[/math] intuitionistic fuzzy modal operators. Annals of Fuzzy Mathematics and Informatics, 13(6), 759–768.
  9. Eker, E., Tugrul, F., & Çitil, M. (2015). New equalities on the intuitionistic fuzzy operators and operations. Notes on Intuitionistic Fuzzy Sets, 21(4), 124–128.
  10. Tarsuslu (Yılmaz), S., Çitil, M., Demirbas, E., & Aydın, M. (2017). Some modal operators with intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 23(5), 20–28.
  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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