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Issue:On the intuitionistic fuzzy modal feeble topological structures

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Title of paper: On the intuitionistic fuzzy modal feeble topological structures
Author(s):
Krassimir Atanassov
Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., Block 105, 1113 Sofia, Bulgaria
krat@bas.bg
Presented at: 25th ICIFS, Sofia, 9—10 September 2022
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 3, pages 211–222
DOI: https://doi.org/10.7546/nifs.2022.28.3.211-222
Download:  PDF (194  Kb, File info)
Abstract: In the paper, for the first time, ideas for intuitionistic fuzzy modal feeble topological structures (of two types) are introduced, and some of their properties are discussed. These topologies are based on the intuitionistic fuzzy operation @, intuitionistic fuzzy operator W, on the two intuitionistic fuzzy modal operators □, ◊ and of simplest intuitionistic fuzzy extended Dα.
Keywords: Intuitionistic fuzzy operation, Intuitionistic fuzzy operator, Intuitionistic fuzzy set, Intuitionistic fuzzy topology.
AMS Classification: 03E72
References:
  1. Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
  2. Atanassov, K. (1988). Two operators on intuitionistic fuzzy sets. Comptes Rendus de l’Academie bulgare des Sciences, 41(5), 35–38.
  3. Atanassov, K. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg.
  4. Atanassov, K. (2012). On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
  5. Atanassov, K. (2017). Intuitionistic Fuzzy Logics. Springer, Cham.
  6. Atanassov, K., & Ban, A. (2000). On an operator over intuitionistic fuzzy sets. Comptes Rendus de l’Academie bulgare des Sciences, 53(5), 39–42.
  7. Blackburn, P., van Bentham, J., & Wolter, F. (2006). Modal Logic. North Holland, Amsterdam.
  8. Bourbaki, N. (1960). Éléments De Mathématique, Livre III: Topologie Générale, Chapitre 1: Structures Topologiques, Chapitre 2: Structures Uniformes. (3rd edition, French). Herman, Paris.
  9. Feys, R. (1965). Modal Logics. Gauthier, Paris.
  10. Fitting, M., & Mendelsohn, R. (1998). First Order Modal Logic. Kluwer, Dordrecht.
  11. Kuratowski, K. (1966). Topology, Vol. 1, New York, Academic Press.
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