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Issue:Relations between some IF modal operators and IF negations

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Title of paper: Relations between some IF modal operators and IF negations
Author(s):
Sinem Tarsuslu
Faculty of Arts and Sciences Department of Mathematics, Mersin University, Mersin, Turkey
sinemnyilmaz@gmail.com
Gökhan Çuvalcioğlu
Faculty of Arts and Sciences Department of Mathematics, Mersin University, Mersin, Turkey
gcuvalcioglu@gmail.com
Yelda Yorulmaz
Faculty of Arts and Sciences Department of Mathematics, Mersin University, Mersin, Turkey
yeldayorulmaz@gmail.com
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 23, 2017, Number 4, pages 31—39
Download:  PDF (176 Kb  Kb, File info)
Abstract: There have been many studies about intuitionistic fuzzy modal operators and intuitionistic fuzzy negations. The relation between some intuitionistic fuzzy modal operators and negations were firstly examined by Hinde and Atanassov [9]. New properties about intuitionistic fuzzy negations &neg;1, &neg;4, &neg;8, &neg;20, &neg;25, &neg;ε with some intuitionistic fuzzy one type, second type and

uni-type modal operators are studied.

Keywords: Intuitionistic fuzzy sets, Intuitionistic fuzzy modal operators, Intuitionistic fuzzy negations.
AMS Classification: 03E72, 47S40
References:
  1. Atanassov, K. T. (1983) Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, June 20-23, (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. (2012) On intuitionistic fuzzy sets theory, Springer, Heidelberg.
  4. Atanassova, V., & Doukovska, L. (2017) Compass-and-straightedge constructions in the intuitionistic fuzzy interpretational triangle: two new intuitionistic fuzzy modal operators, Notes on IFS, 23(2), 1–7.
  5. Çuvalcioğlu, G. (2007) Some Properties of Eα,β operator, Advanced Studies on Contemporary Mathematics, 14(2), 305–310.
  6. Çuvalcioğlu, 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.
  7. Çuvalcioğlu, G. (2016) One, two and uni-type operators on IFSs, Studies in Fuzziness and Soft Computing, 332, 55–71.
  8. Dencheva, K. (2004) Extension of intuitionistic fuzzy modal operators ⊞ and ⊠, Proc.of the Second Int. IEEE Symp. Intelligent systems, 3, 21–22.
  9. Hinde, C., & Atanassov, K. T. (2007) Intuitionistic fuzzy negations and intuitionistic fuzzy modal operators. Notes on IFS, 13(4), 41–44.
  10. Jamkhaneh, E. B., & Ghara, A. N. (2017) Four new operators over the generalized intuitionistic fuzzy sets, Journal of New Theory, 18, 12–21.
  11. Nagalingam, R., & Rajaram, S. (2017) New intuitionistic fuzzy operator A(m,n) and an application on decision making, Advances in Fuzzy Mathematics, 12(4), 881–895.
  12. Yılmaz, S., & Çuvalcioğlu, G., Intuitionistic fuzzy modal operators: Sα,β and Tα,β. 28th National Mathematical Symposium, Antalya, 07-09 September 2015.
  13. Yılmaz, S., & Bal, A. (2014) Extension of intuitionistic fuzzy modal operators diagram with new operators, Notes on IFS, 20(5), 26–35.
  14. Zadeh, L. A. (1965) Fuzzy Sets, Information and Control, 8, 338–353.
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