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Issue:Intuitionistic fuzzy interpretation of a classical formula: Difference between revisions

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  | format          = PDF
  | format          = PDF
  | size            = 179
  | size            = 179
  | abstract        = The formula <math>\neg A = (A \rightarrow ((A \rightarrow A) \wedge \neg (A \rightarrow A)))</math> is a tautology in the classical propositional logic. In this paper, we determine all intuitionistic fuzzy implications that satisfy this formula together with the classical intuitionistic fuzzy negation or with the negation generated by this implication
  | abstract        = The formula <math>\neg A = (A \rightarrow ((A \rightarrow A) \wedge \neg (A \rightarrow A)))</math> is a tautology in the classical propositional logic. In this paper, we determine all intuitionistic fuzzy implications that satisfy this formula together with the classical intuitionistic fuzzy negation or with the negation generated by this implication.
  | keywords        = Intuitionistic fuzzy implication, Intuitionistic fuzzy negation, Tautology.
  | keywords        = Intuitionistic fuzzy implication, Intuitionistic fuzzy negation, Tautology.
  | ams            = 03E72.
  | ams            = 03E72.
Line 53: Line 53:
# Atanassova, L. (2014). Remark on the intuitionistic fuzzy forms of two classical logic axioms. Part 1. Annual of the “Informatics” Section, Union of Scientists in Bulgaria, 7, 24–27.
# Atanassova, L. (2014). Remark on the intuitionistic fuzzy forms of two classical logic axioms. Part 1. Annual of the “Informatics” Section, Union of Scientists in Bulgaria, 7, 24–27.
# Atanassova, L. (2014). [[Issue:Remark on the intuitionistic fuzzy forms of two classical logic axioms. Part 2|Remark on the intuitionistic fuzzy forms of two classical logic axioms. Part 2]]. Notes on Intuitionistic Fuzzy Sets, 20(4), 10–13.
# Atanassova, L. (2014). [[Issue:Remark on the intuitionistic fuzzy forms of two classical logic axioms. Part 2|Remark on the intuitionistic fuzzy forms of two classical logic axioms. Part 2]]. Notes on Intuitionistic Fuzzy Sets, 20(4), 10–13.
# Michalíková, A., Szmidt, E., & Vassilev, P. (2021). [[Issue:Modifications of Lukasiewicz’s intuitionistic fuzzy implication|Modifications of Łukasiewicz's  intuitionistic fuzzy implication]]. Notes on Intuitionistic Fuzzy Sets, 27(3), 32–39.
# Michalíková, A., Szmidt, E., & Vassilev, P. (2021). [[Issue:Modifications_of_Łukasiewicz's_intuitionistic_fuzzy_implication|Modifications_of_Łukasiewicz's_intuitionistic_fuzzy_implication]]. Notes on Intuitionistic Fuzzy Sets, 27(3), 32–39.
# Nakamatsu, K. (2008). The paraconsistent annotated logic program EVALPSN and its application. In: Fulcher, J., & Jain, L. (Eds.). Computational Intelligence: A Compendium. Springer, Berlin, 233–306.
# Nakamatsu, K. (2008). The paraconsistent annotated logic program EVALPSN and its application. In: Fulcher, J., & Jain, L. (Eds.). Computational Intelligence: A Compendium. Springer, Berlin, 233–306.
#  Vassilev, P., Ribagin, S., & Kacprzyk, J. (2018). [[Issue:A remark on intuitionistic fuzzy implications|A remark on intuitionistic fuzzy implications]]. Notes on Intuitionistic Fuzzy Sets, 24(2), 1–7.
#  Vassilev, P., Ribagin, S., & Kacprzyk, J. (2018). [[Issue:A remark on intuitionistic fuzzy implications|A remark on intuitionistic fuzzy implications]]. Notes on Intuitionistic Fuzzy Sets, 24(2), 1–7.

Latest revision as of 10:23, 30 November 2025

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http://ifigenia.org/wiki/issue:nifs/31/4/427-440
Title of paper: Intuitionistic fuzzy interpretation of a classical formula
Author(s):
Krassimir Atanassov     0000-0001-5625-071X
Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia–1113, Bulgaria
krat@bas.bg , k.t.atanassov@gmail.com
Nora Angelova     0000-0003-2697-9766
Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
noraa@fmi.uni-sofia.bg
Janusz Kacprzyk     0000-0003-4187-5877
System Research Institute, Polish Academy of Sciences, Newelska, 6, 01-447, Warsaw, Poland
janusz.kacprzyk@ibspan.waw.pl
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 4, pages 427–440
DOI: https://doi.org/10.7546/nifs.2025.31.4.427-440
Download:  PDF (179  Kb, File info)
Abstract: The formula [math]\displaystyle{ \neg A = (A \rightarrow ((A \rightarrow A) \wedge \neg (A \rightarrow A))) }[/math] is a tautology in the classical propositional logic. In this paper, we determine all intuitionistic fuzzy implications that satisfy this formula together with the classical intuitionistic fuzzy negation or with the negation generated by this implication.
Keywords: Intuitionistic fuzzy implication, Intuitionistic fuzzy negation, Tautology.
AMS Classification: 03E72.
References:
  1. Angelova, N., & Atanassov, K. (2021). Research on intuitionistic fuzzy implications. Notes on Intuitionistic Fuzzy Sets, 27(2), 20–93.
  2. Angelova, N., Atanassov, K., & Atanassova, V. (2022). Research on intuitionistic fuzzy implications. Part 2. Notes on Intuitionistic Fuzzy Sets, 28(2), 172–192.
  3. Angelova, N., Atanassov, K., & Atanassova, V. (2023). Research on intuitionistic fuzzy implications. Part 3. Notes on Intuitionistic Fuzzy Sets, 29(4), 365–370.
  4. Angelova, N., Atanassov, K., & Atanassova, V. (2024). Research on intuitionistic fuzzy implications. Part 4. Notes on Intuitionistic Fuzzy Sets, 30(1), 1–8.
  5. Angelova, N., Čunderlíková, K., Szmidt, E., & Atanassov, K. (2022). Intuitionistic fuzzy interpretations of formula (A → B) → ((¬A → B) → B). Notes on Intuitionistic Fuzzy Sets, 28(4), 428-–435.
  6. Atanassov, K. (1988). Two variants of intuitionistic fuzzy propositional calculus. Preprint. IM-MFAIS-5-88, Sofia;. Reprinted: International Journal Bioautomation, 2016, 20(S1), S17–S26.
  7. Atanassov, K. (2017). Intuitionistic Fuzzy Logics. Springer, Cham.
  8. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2013). On intuitionistic fuzzy pairs. Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13.
  9. Atanassov, K., Szmidt, E., Kacprzyk, J. & Angelova, N. (2019) Intuitionistic fuzzy implications revisited. Part 1. Notes on Intuitionistic Fuzzy Sets, 25(3), 71-–78.
  10. Atanassova, L. (2013). On the intuitionistic fuzzy form of the classical implication (A → B) ∨ (B → A). Notes on Intuitionistic Fuzzy Sets, 19(4), 15-—18.
  11. Atanassova, L. (2014). Remark on the intuitionistic fuzzy forms of two classical logic axioms. Part 1. Annual of the “Informatics” Section, Union of Scientists in Bulgaria, 7, 24–27.
  12. 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.
  13. Michalíková, A., Szmidt, E., & Vassilev, P. (2021). Modifications_of_Łukasiewicz's_intuitionistic_fuzzy_implication. Notes on Intuitionistic Fuzzy Sets, 27(3), 32–39.
  14. Nakamatsu, K. (2008). The paraconsistent annotated logic program EVALPSN and its application. In: Fulcher, J., & Jain, L. (Eds.). Computational Intelligence: A Compendium. Springer, Berlin, 233–306.
  15. Vassilev, P., Ribagin, S., & Kacprzyk, J. (2018). A remark on intuitionistic fuzzy implications. Notes on Intuitionistic Fuzzy Sets, 24(2), 1–7.
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