Issue:Intuitionistic fuzzy interpretation of a classical formula

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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: Angelova, N., & Atanassov, K. (2021). Research on intuitionistic fuzzy implications. Notes on Intuitionistic Fuzzy Sets, 27(2), 20–93. Angelova, N., Atanassov, K., & Atanassova, V. (2022). Research on intuitionistic fuzzy implications. Part 2. Notes on Intuitionistic Fuzzy Sets, 28(2), 172–192. Angelova, N., Atanassov, K., & Atanassova, V. (2023). Research on intuitionistic fuzzy implications. Part 3. Notes on Intuitionistic Fuzzy Sets, 29(4), 365–370. Angelova, N., Atanassov, K., & Atanassova, V. (2024). Research on intuitionistic fuzzy implications. Part 4. Notes on Intuitionistic Fuzzy Sets, 30(1), 1–8. 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. 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. Atanassov, K. (2017). Intuitionistic Fuzzy Logics. Springer, Cham. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2013). On intuitionistic fuzzy pairs. Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13. Atanassov, K., Szmidt, E., Kacprzyk, J. & Angelova, N. (2019) Intuitionistic fuzzy implications revisited. Part 1. Notes on Intuitionistic Fuzzy Sets, 25(3), 71-–78. 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. 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 2. Notes on Intuitionistic Fuzzy Sets, 20(4), 10–13. Michalíková, A., Szmidt, E., & Vassilev, P. (2021). 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. Vassilev, P., Ribagin, S., & Kacprzyk, J. (2018). A remark on intuitionistic fuzzy implications. Notes on Intuitionistic Fuzzy Sets, 24(2), 1–7. 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.