As of August 2024, International Journal "Notes on Intuitionistic Fuzzy Sets" is being indexed in Scopus.
Please check our Instructions to Authors and send your manuscripts to nifs.journal@gmail.com. Next issue: September/October 2024.
Open Call for Papers: International Workshop on Intuitionistic Fuzzy Sets • 13 December 2024 • Banska Bystrica, Slovakia/ online (hybrid mode).
Deadline for submissions: 16 November 2024.

Issue:A general approach to modal topological structures illustrated by intuitionistic fuzzy objects

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Revision as of 10:31, 27 October 2024 by Vassia Atanassova (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
shortcut
http://ifigenia.org/wiki/issue:nifs/30/3/260-284
Title of paper: A general approach to modal topological structures illustrated by intuitionistic fuzzy objects
Author(s):
Krassimir Atanassov
Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineerings, Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., Block 105, Sofia 1113, Bulgaria
krat@bas.bg
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 30 (2024), Number 3, pages 260–284
DOI: https://doi.org/10.7546/nifs.2024.30.3.260-284
Download:  PDF (251  Kb, File info)
Abstract: A new, general approach to introducing of the concept of a Modal Topological Structure (MTS) is given. The basic properties of the MTS are studied. The MTSs are illustrated by intuitionistic fuzzy objects - intuitionistic fuzzy sets, operations, relations and operators. So, 38 different intuitionistic fuzzy MTSs are described.
Keywords: Intuitionistic fuzzy set, Intuitionistic fuzzy modal topological structure.
AMS Classification: 03E72
References:
  1. Atanassov, K. (1999). Intuitionistic Fuzzy Sets. Springer, Heidelberg.
  2. Atanassov, K. (2012). On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
  3. Atanassov, K. (2022). Intuitionistic fuzzy modal topological structure. Mathematics, 10, Article 3313.
  4. Atanassov, K. (2022). On intuitionistic fuzzy modal topological structures with modal operator of second type. Notes on Intuitionistic Fuzzy Sets, 28(4), 457–463.
  5. Atanassov, K. (2022). On four intuitionistic fuzzy feeble topological structures. Proceedings of 11th IEEE International Conference on Intelligent Systems (IS), Warsaw, 12-14 Oct. 2022. DOI: 10.1109/IS57118.2022.10019726
  6. Atanassov, K. (2022). On the intuitionistic fuzzy modal feeble topological structures. Notes on Intuitionistic Fuzzy Sets, 28(3), 211–222.
  7. Atanassov, K. (2023). Four new intuitionistic fuzzy bimodal topological structures. Notes on Intuitionistic Fuzzy Sets, 29(3), 239–246.
  8. Atanassov, K. (2023). Intuitionistic fuzzy modal topological structures based on two new intuitionistic fuzzy modal operators. Journal of Multiple-Valued Logic & Soft Computing, 41, 227–240.
  9. Atanassov, K. (2023). On intuitionistic fuzzy extended modal topological structures. In: Atanassov, K., et al (Eds.). Uncertainty and Imprecision in Decision Making and Decision Support – New Advances, Challenges, and Perspectives, Springer, Cham, 2023, 3–14.
  10. Atanassov, K. (2023). On intuitionistic fuzzy temporal topological structures. Axioms, 12, Article 182.
  11. Atanassov, K. (2023). On two new intuitionistic fuzzy topological operators and four new intuitionistic fuzzy feeble modal topological structures. Notes on Intuitionistic Fuzzy Sets, 29(1), 74–83.
  12. Atanassov, K. (2024). Intuitionistic fuzzy modal multi-topological structures and intuitionistic fuzzy multi-modal multi-topological structures. Mathematics, 12, Article 361.
  13. Atanassov, K., Angelova, N., & Pencheva, T. (2023). On two intuitionistic fuzzy modal topological structures. Axioms, 12, Article 408.
  14. Ban, A. I. (1997). Convex intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 3(2), 66–76.
  15. Blackburn, P., van Bentham, J., & Wolter, F. (2006). Modal Logic. North Holland, Amsterdam.
  16. Bourbaki, N. (1960). Elements De Mathematique, Livre III: Topologie Generale (3rd Ed.). Chapitre 1: Structures Topologiques, Chapitre 2: Structures Uniformes. Herman, Paris (in French).
  17. Çoker, D. (1997). An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems, 88(1), 81–89.
  18. Çoker, D. (1997). On topological structures using intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 3(5), 138–142.
  19. Çoker, D., & Demirci, M. (1995). An introduction to intuitionistic fuzzy points. Notes on Intuitionistic Fuzzy Sets, 1(2), 79–84.
  20. Çoker, D., Demirci, M. (1996). An introduction to intuitionistic topological spaces in Sostak’s sense. BUSEFAL, 67, 67–76.
  21. El-Latif, A., & Khalaf, M. (2015). Connectedness in intuitionistic fuzzy topological spaces in Sostak’s sense. Italian Journal of Pure and Applied Mathematics, 35, 649–668.
  22. Feys, R. (1965). Modal Logics, Gauthier, Paris.
  23. Fitting, M., & Mendelsohn, R. (1998). First Order Modal Logic. Kluwer, Dordrecht.
  24. Haydar Es¸, A., & Çoker, D. (1996). More on fuzzy compactness in intuitionistic fuzzy topological spaces. Notes on Intuitionistic Fuzzy Sets, 2(1), 4–10.
  25. Kim, Y. C., & Abbas, S. E. (2005). Connectedness in intuitionistic fuzzy topological spaces. Communications of the Korean Mathematical Society, 20(1), 117–134.
  26. Kuratowski, K. (1966). Topology, Vol. 1, New York, Academic Press.
  27. Kutlu, F. (2017). On separation axioms in temporal intuitionistic fuzzy Sostak topology. Notes on Intuitionistic Fuzzy Sets, 23(1), 21–30.
  28. Kutlu, F., Atan, O., & Bilgin, T. (2016). Distance measure, similarity measure. Entropy and inclusion measure for temporal intuitionistic fuzzy sets. In: Proceedings of IFSCOM’2016, Mersin, Turkey, 130–148.
  29. Kutlu, F., & Bilgin, T. (2015). Temporal intuitionistic fuzzy topology in Sostak’s sense. Notes on Intuitionistic Fuzzy Sets, 21(2), 63–70.
  30. Kutlu, F., Ramadan, A., & Bilgin, T. (2016). On compactness in temporal intuitionistic fuzzy sostak topology. Notes on Intuitionistic Fuzzy Sets, 22(5), 46–62.
  31. Lee, S. J., & Lee, E. P. (2000). The category of intuitionistic fuzzy topological spaces. Bulletin of Korean Mathematical Society, 37(1), 63–76.
  32. Lupianez, F. G. (2004). Separation in intuitionistic fuzzy topological spaces. International Journal of Pure and Applied Mathematics, 17(1), 29–34.
  33. Lupianez, F. G. (2006). On intuitionistic fuzzy topological spaces. Kybernetes, 35(5–6), 743–747.
  34. Milles, S. (2020). The lattice of intuitionistic fuzzy topologies generated by intuitionistic fuzzy relations. Applications and Applied Mathematics, 15(2), 942–956.
  35. Mints, G. (1992). A Short Introduction to Modal Logic. University of Chicago Press, Chicago.
  36. Mondal, K., & Samanta, S. K. (2003). A study on intuitionistic fuzzy topological spaces. Notes on Intuitionistic Fuzzy Sets, 9(1), 1–32.
  37. Munkres, J. (2000). Topology. Prentice Hall Inc., New Jersey.
  38. Ozbakir, O., & Çoker, D. (1999). Fuzzy multifunctions in intuitionistic fuzzy topological spaces. Notes on Intuitionistic Fuzzy Sets, 5(3), 1–5.
  39. Park, J. H. (2004). Intuitionistic fuzzy metric spaces. Chaos Solitons Fractals, 22(5), 1039–1046.
  40. Rajarajeswari, P., & Krishna Moorthy, R. (2012). Intuitionistic fuzzy completely weakly generalized continuous mappings. Notes on Intuitionistic Fuzzy Sets, 18(1), 25–36.
  41. Roopkumar, R., & Kalaivani, C. (2010). Continuity of intuitionistic fuzzy proper functions on intuitionistic smooth fuzzy topological spaces. Notes on Intuitionistic Fuzzy Sets, 16(3), 1–21.
  42. Saadati, R., Park, J. H. (2006). On the intuitionistic fuzzy topological spaces. Chaos Solitons Fractals, 27(2), 331–334.
  43. Samanta, S. K., & Mondal, T. K. (1997). Intuitionistic gradation of openness: Intuitionistic fuzzy topology. BUSEFAL, 73, 8–17.
  44. Thakur, S., & Chaturvedi, R. (2006). Generalized continuity in intuitionistic fuzzy topological spaces. Notes on Intuitionistic Fuzzy Sets, 12(1), 38–44.
  45. Tiwari, S. (2010). On relationships among intuitionistic fuzzy approximation operators, intuitionistic fuzzy topology and intuitionistic fuzzy automata. Notes on Intuitionistic Fuzzy Sets, 16(1), 1–9.
  46. Yılmaz, S., & Cuvalcıoglu, G. (2014). On level operators for temporal intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 20(2), 6–15.
  47. Yongfa, H., & Changjun, J. (2004). Some properties of intuitionistic fuzzy metric spaces. Notes on Intuitionistic Fuzzy Sets, 10(1), 18–26.
Citations:

The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.

Retrieved from "https://ifigenia.org/index.php?title=Issue:A_general_approach_to_modal_topological_structures_illustrated_by_intuitionistic_fuzzy_objects&oldid=13636"