Submit your research to the International Journal "Notes on Intuitionistic Fuzzy Sets". Contact us at nifs.journal@gmail.com

Call for Papers for the 25th Jubilee Edition of the International Conference on Intuitionistic Fuzzy Sets is now open!
Conference: 9–10 September 2022 • Deadline for submission: 30 May 2022.

Issue:Research on intuitionistic fuzzy negations

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Jump to navigation Jump to search
shortcut
http://ifigenia.org/wiki/issue:nifs/27/3/18-31
Title of paper: Research on intuitionistic fuzzy negations
Author(s):
Nora Angelova
Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
noraa@fmi.uni-sofia.bg
Krassimir T. Atanassov
Dept. of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria
krat@bas.bg
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 3, pages 18–31
DOI: https://doi.org/10.7546/nifs.2021.27.3.18-31
Download: Download-icon.png PDF (178  Kb, Info)
Abstract: In the theories of intuitionistic fuzzy sets and intuitionistic fuzzy logics, there are 54 different negations. Here, we check the relationship between every two of them.
Keywords: Intuitionistic fuzzy negation, Intuitionistic fuzzy implication, Intuitionistic fuzzy pair, Intuitionistic fuzzy set.
AMS Classification: 03E72.
References:
  1. Angelova, N. (2019). IFSTool – Software for intuitionistic fuzzy sets – Necessity, Possibility and Circle operators. Advances in Intelligent Systems and Computing, issue:1081, Publisher:Springer, 76–81.
  2. Angelova, N., & Atanassov, K. (2015). Intuitionistic Fuzzy Implications and the Axioms of Intuitionistic Logic. In: Proc. of the 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), 30.06-03.07.2015, Gijon, Spain, 1578–1584.
  3. Angelova, N., & Atanassov, K. (2016). Intuitionistic Fuzzy Implications and Klir–Yuan’s Axioms. Novel Developments in Uncertainty Representation and Processing. Advances in Intuitionistic Fuzzy Sets and Generalized Nets, Advances in Intelligent Systems and Computing, 401. Atanassov, K.T., Castillo, O., Kacprzyk, J., Krawczak, M., Melin, P., Sotirov, S., Sotirova, E., Szmidt, E., De Tr´e, G., Zadro˙zny, S. (Eds.), 97–110.
  4. Angelova, N., & Atanassov, K. (2021). Research on intuitionistic fuzzy implications. Notes on Intuitionistic Fuzzy Sets, 27(2), 20–93.
  5. Angelova, N., Marinov, E., & Atanassov, K. (2015). Intuitionistic fuzzy implications and Kolmogorov’s and Łukasiewisz–Tarski’s axioms of logic. Notes on Intuitionistic Fuzzy Sets, 21(2), 35–42.
  6. Atanassov, K. (1988). Two variants of intuitonistic fuzzy propositional calculus. Preprint IM-MFAIS-5-88, Sofia.
  7. Atanassov, K. (2005). On some intuitionistic fuzzy negations. Proc. of the First Int. Workshop on IFSs, Banska Bystrica, 22 Sept. 2005. Notes on Intuitionistic Fuzzy Sets, 11(6), 13–20.
  8. Atanassov, K. (2006). A new intuitionistic fuzzy implication from a modal type. Advanced Studies on Contemporary Mathematics, 12 (1), 117–122.
  9. Atanassov, K. (2006). On eight new intuitionistic fuzzy implications. Proc. of 3rd Int. IEEE Conf. “Intelligent Systems” IS06, London, 4-6 Sept. 2006, 741–746.
  10. Atanassov, K. (2006). On some intuitionistic fuzzy implications. Comptes Rendus de l’Academie bulgare des Sciences, 59(1), 19–24.
  11. Atanassov, K. (2008). On intuitionistic fuzzy implication →[math]\displaystyle{ ^\epsilon }[/math] and intuitionistic fuzzy negation ¬[math]\displaystyle{ ^\epsilon }[/math]. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 6, 6–19.
  12. Atanassov, K. (2008). Intuitionistic fuzzy implication →[math]\displaystyle{ ^{\epsilon, \eta} }[/math] and intuitionistic fuzzy negation ¬[math]\displaystyle{ ^{\epsilon, \eta} }[/math]. Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, 1, 1–10.
  13. Atanassov, K. (2011). Second Zadeh’s intuitionistic fuzzy implication. Notes on Intuitionistic Fuzzy Sets, 17(3), 11–14.
  14. Atanassov, K. (2012). On Intuitionistic Fuzzy Sets Theory, Springer, Berlin.
  15. Atanassov, K. (2015). On a new intuitionistic fuzzy implication. In: Proc of the 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), 30.06-03.07.2015, Gijon, Spain, 1592–1597.
  16. Atanassov, K. (2016). On intuitionistic fuzzy implications. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 12, 1–19.
  17. Atanassov, K. (2017). Intuitionistic Fuzzy Logics, Springer, Cham.
  18. Atanassov, K (2021). Third Zadeh’s Intuitionistic Fuzzy Implication. Mathematics, 9(6), 619.
  19. Atanassov, K., & Angelova, N. (2021). Modifications of the Third Zadeh’s intuitionistic fuzzy implication. Notes on Intuitionistic Fuzzy Sets, 27(1), 9 -23.
  20. Atanassov, K., & Angelova, N. (2016). Properties of intuitionistic fuzzy implications and negations. Notes on Intuitionistic Fuzzy Sets, 22(3), 25–33.
  21. Atanassov, K., Angelova, N.& Atanassova, V. (2021). On an Intuitionistic Fuzzy Form of the Goguen’s Implication. Mathematics, 9(6), 676.
  22. Atanassov, K., & Dimitrov, D. (2010). Intuitionistic fuzzy implications and axioms for implications. Notes in Intuitionistic Fuzzy Sets, 16(1), 10–20.
  23. Atanassov, K., Ribagin, S., Doukovska, L., & Atanassova, V. (2017). Intuitionistic fuzzy →[math]\displaystyle{ _{190} }[/math]. Notes on Intuitionistic Fuzzy Sets, 23(4), 79–83.
  24. Atanassov, K., & Szmidt, E. (2014). Remark on intuitionistic fuzzy implication →[math]\displaystyle{ ^{\epsilon, \eta} }[/math]. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 11, 9–14.
  25. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2013). On intuitionistic fuzzy pairs, Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13.
  26. Atanassov, K., Szmidt, E. & Kacprzyk, J. (2015). On Fodor’s type of intuitionistic fuzzy implication and negation. Notes on Intuitionistic Fuzzy Sets, 21(2), 25–34.
  27. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2016). New Fodor’s Type Of Intuitionistic Fuzzy Implication and Negation. Notes on Intuitionistic Fuzzy Sets, 22(3), 1–8.
  28. Atanassov, K., Szmidt, E., Kacprzyk, J., & Angelova, N. (2019). Intuitionistic fuzzy implications revisited. Part 1. Notes on Intuitionistic Fuzzy Sets, 25(3), 71–78.
  29. Atanassov, K., & Trifonov, T. (2005). On a new intuitionistic fuzzy implication of Godel’s type. Proceedings of the Jangjeon Mathematical Society, 8(2), 147–152.
  30. Atanassov, K., & Trifonov, T. (2006). Two new intuitionistic fuzzy implications. Advanced Studies on Contemporary Mathematics, 13(1), 69–74.
  31. Atanassova, L. (2008). On an intuitionistic fuzzy implication from Kleene-Dienes type. Proceedings of the Jangjeon Mathematical Society, 11(1), 69–74.
  32. Atanassova, L. (2008). Modifications of an intuitionistic fuzzy implication from Kleene-Dienes type. Advanced Studies in Contemporary Mathematics, 16 (2), 155–160.
  33. Atanassova, L. (2008). New modifications of an intuitionistic fuzzy implication from Kleene-Dienes type. Part 2. Annual of Section “Informatics”, 1, 59–64.
  34. Atanassova, L. (2009). New modifications of an intuitionistic fuzzy implication from Kleene-Dienes type. Part 3. Advanced Studies in Contemporary Mathematics, 18 (1), 33–40.
  35. Atanassova, L. (2009). A new intuitionistic fuzzy implication. Cybernetics and Information Technologies, 9(2), 21–25.
  36. Atanassova, L. (2009). On some properties of intuitionistic fuzzy negation ¬@. Notes on Intuitionistic Fuzzy Sets, 15(1), 32–35.
  37. Atanassova, L. (2012). On two modifications of the intuitionistic fuzzy implication →@. Notes on Intuitionistic Fuzzy Sets, 18(2), 26–30
  38. Atanassova, L. (2013). On the modal form of the intuitionistic fuzzy implications →'@ and →@. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 10, 5–11.
  39. Atanassova, L. (2013). On the intuitionistic fuzzy form of the classical implication [math]\displaystyle{ (A \rightarrow B)\vee(B\rightarrow A) }[/math]. Notes on Intuitionistic Fuzzy Sets, 19(4), 15–18.
  40. Atanassova, L. (2014). Remark on the intuitionistic fuzzy forms of two classical logic axioms. Part 1. Annual of Section “Informatics”, 7, 24–27.
  41. Atanassova, L. (2014). Remark on the intuitionistic fuzzy forms of two classical logic axioms. Part 2. Notes on Intuitionistic Fuzzy Sets, 20(4), 10–13.
  42. Atanassova, L. (2015). Remark on Dworniczak’s intuitionistic fuzzy implications. Part 1. Notes on Intuitionistic Fuzzy Sets, 21(3), 18–23.
  43. Atanassova, L. (2015). Remark on Dworniczak’s intuitionistic fuzzy implications. Part 2. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 12, 61–67.
  44. Atanassova, L. (2016). Remark on Dworniczak’s intuitionistic fuzzy implications. Part 3. Notes on Intuitionistic Fuzzy Sets, 22(1), 1–6.
  45. Atanassova, L. (2017). Properties of the intuitionistic fuzzy implication →189. Notes on Intuitionistic Fuzzy Sets, 23(4), 10–14.
  46. Dworniczak, P. (2010). Some remarks about the L. Atanassova’s paper “A new intuitionistic fuzzy implication”, Cybernetics and Information Technologies, 10(3), 3–9.
  47. Dworniczak, P. (2010). On one class of intuitionistic fuzzy implications. Cybernetics and Information Technologies, 10(4), 13–21.
  48. Dworniczak, P. (2011). On some two-parametric intuitionistic fuzzy implication. Notes on Intuitionistic Fuzzy Sets, 17(2), 8–16.
  49. Klir, G., & Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic. Prentice Hall, New Jersey.
  50. Szmidt, E., Kacprzyk, J., & Atanassov, K. (2015). Properties of Fodor’s intuitionistic fuzzy implication and negation. Notes on Intuitionistic Fuzzy Sets, 21(4), 6–12.
  51. Szmidt, E., Kacprzyk, J., & Atanassov, K. (2015). Modal forms of Fodor’s type of intuitionistic fuzzy implication. Notes on Intuitionistic Fuzzy Sets, 21(5), 1–5.
  52. Vassilev, P., & Atanassov, K. (2019). Extensions and Modifications of Intuitionistic Fuzzy Sets. “Prof. Marin Drinov” Academic Publishing House, Sofia.
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.