| Title of paper:
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Intuitionistic fuzzy interpretation of a classical formula
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| Author(s):
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Krassimir Atanassov  0000-0001-5625-071X
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| 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
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| krat@bas.bg , k.t.atanassov@gmail.com
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| Nora Angelova 0000-0003-2697-9766
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| Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
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| noraa@fmi.uni-sofia.bg
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| Janusz Kacprzyk 0000-0003-4187-5877
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| System Research Institute, Polish Academy of Sciences, Newelska, 6, 01-447, Warsaw, Poland
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| janusz.kacprzyk@ibspan.waw.pl
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 4, pages 427–440
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| DOI:
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https://doi.org/10.7546/nifs.2025.31.4.427-440
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| Download:
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 PDF (179 Kb, File info)
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| Abstract:
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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
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| Keywords:
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Intuitionistic fuzzy implication, Intuitionistic fuzzy negation, Tautology.
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| AMS Classification:
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03E72.
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| References:
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- 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.
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