Issue:Intuitionistic fuzzy interpretation of a classical formula - Revision history

Vassia Atanassova: .

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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.

Vassia Atanassova at 21:03, 27 November 2025

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	# 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 Łukasiewicz’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.

Vassia Atanassova at 21:02, 27 November 2025

2025-11-27T21:02:14Z

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	# 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.

Vassia Atanassova at 21:01, 27 November 2025

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	\| format = PDF		\| format = PDF
	\| size = 179		\| size = 179
	\| abstract = The formula		\| 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
	<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.

Vassia Atanassova at 21:01, 27 November 2025

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	}}		}}
	{{issue/data		{{issue/data
	\| issue = [[Notes on Intuitionistic Fuzzy Sets/31/3\|Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 3]], pages ~~372–385~~		\| issue = [[Notes on Intuitionistic Fuzzy Sets/31/4\|Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 4]], pages 427–440
	\| doi = https://doi.org/10.7546/nifs.2025.31.3.~~372~~-~~385~~		\| doi = https://doi.org/10.7546/nifs.2025.31.4.427-440
	\| file = NIFS-31-3-~~372~~-~~385~~.pdf		\| file = NIFS-31-4-427-440.pdf
	\| format = PDF		\| format = PDF
	\| size = ~~563~~		\| size = 179
	\| abstract = The formula		\| abstract = The formula
	<math>\neg A = (A \rightarrow ((A \rightarrow A) \wedge \neg (A \rightarrow A)))</math>		<math>\neg A = (A \rightarrow ((A \rightarrow A) \wedge \neg (A \rightarrow A)))</math>

Vassia Atanassova: Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}} {{issue/title | title = Intuitionistic fuzzy interpretation of a classical formula | shortcut = nifs/31/4/427-440 }} {{issue/author | author = Krassimir Atanassov | institution = Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Bio..."

2025-11-27T20:52:11Z

Created page with "{{PAGENAME}} {{PAGENAME}} {{PAGENAME}} {{issue/title | title = Intuitionistic fuzzy interpretation of a classical formula | shortcut = nifs/31/4/427-440 }} {{issue/author | author = Krassimir Atanassov | institution = Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Bio..."

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[[Category:Publications on intuitionistic fuzzy sets|{{PAGENAME}}]]
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[[Category:Publications in 2025 year|{{PAGENAME}}]]
{{issue/title
| title = Intuitionistic fuzzy interpretation of a classical formula | shortcut = nifs/31/4/427-440
}}
{{issue/author
| author = Krassimir Atanassov
| institution = Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
| address = Acad. G. Bonchev Str., Bl. 105, Sofia–1113, Bulgaria
| email-before-at = krat
| email-after-at = bas.bg
| orcid = 0000-0001-5625-071X
| sec-email-before-at = k.t.atanassov
| sec-email-after-at = gmail.com
}}
{{issue/author
| author = Nora Angelova
| institution = Faculty of Mathematics and Informatics, Sofia University
| address = 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
| email-before-at = noraa
| email-after-at = fmi.uni-sofia.bg
| orcid = 0000-0003-2697-9766
}}
{{issue/author
| author = Janusz Kacprzyk
| institution = System Research Institute, Polish Academy of Sciences
| address = Newelska, 6, 01-447, Warsaw, Poland
| email-before-at = janusz.kacprzyk
| email-after-at = ibspan.waw.pl
| orcid = 0000-0003-4187-5877
}}
{{issue/data
| issue = [[Notes on Intuitionistic Fuzzy Sets/31/3|Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 3]], pages 372–385
| doi = https://doi.org/10.7546/nifs.2025.31.3.372-385
| file = NIFS-31-3-372-385.pdf
| format = PDF
| size = 563
| 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.
| ams = 03E72.
| references =
# Angelova, N., & Atanassov, K. (2021). [[Issue:Research on intuitionistic fuzzy implications|Research on intuitionistic fuzzy implications]]. Notes on Intuitionistic Fuzzy Sets, 27(2), 20–93.
# Angelova, N., Atanassov, K., & Atanassova, V. (2022). [[Issue:Research on intuitionistic fuzzy implications. Part 2|Research on intuitionistic fuzzy implications. Part 2]]. Notes on Intuitionistic Fuzzy Sets, 28(2), 172–192.
# Angelova, N., Atanassov, K., & Atanassova, V. (2023). [[Issue:Research on intuitionistic fuzzy implications. Part 3|Research on intuitionistic fuzzy implications. Part 3]]. Notes on Intuitionistic Fuzzy Sets, 29(4), 365–370.
# Angelova, N., Atanassov, K., & Atanassova, V. (2024). [[Issue:Research on intuitionistic fuzzy implications. Part 4|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). [[Issue:Intuitionistic fuzzy interpretations of formula (A → B) → ((¬A → B) → B)|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). [[Issue:On intuitionistic fuzzy pairs|On intuitionistic fuzzy pairs]]. Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13.
# Atanassov, K., Szmidt, E., Kacprzyk, J. & Angelova, N. (2019) [[Issue:Intuitionistic fuzzy implications revisited. Part 1|Intuitionistic fuzzy implications revisited. Part 1]]. Notes on Intuitionistic Fuzzy Sets, 25(3), 71-–78.
# Atanassova, L. (2013). [[Issue:On the intuitionistic fuzzy form of the classical implication (A → B) ∨ (B → A)|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). [[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.
# 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.

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