Issue:Intuitionistic fuzzy implications revisited. Part 1

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Title of paper: Intuitionistic fuzzy implications revisited. Part 1 Author(s): Krassimir Atanassov 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 Intelligent Systems Laboratory, Prof. Asen Zlatarov University, Burgas 8010, Bulgaria krat@bas.bg Eulalia Szmidt Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland Warsaw School of Information Technology, ul. Newelska 6, 01-447 Warsaw, Poland szmidt@ibspan.waw.pl Janusz Kacprzyk Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland Warsaw School of Information Technology, ul. Newelska 6, 01-447 Warsaw, Poland kacprzyk@ibspan.waw.pl Nora Angelova Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., Sofia 1164, Bulgaria nora.angelova@fmi.uni-sofia.bg Published in: Notes on Intuitionistic Fuzzy Sets, Volume 25 (2019), Number 3, pages 71–78 DOI: 10.7546/nifs.2019.25.3.71-78 Download:  PDF (137  Kb, File info) Abstract: Definitions of two intuitionistic fuzzy implications, published during the last 15 years, are revisited. It is checked which existing by the moment intuitionistic fuzzy implications (190 in number) satisfy a well-known tautology in first order logic. Keywords: Intuitionistic fuzzy implication, Intuitionistic fuzzy logic. AMS Classification: 03E72. References: Andonov, V. (2008). On some properties of one Cartesian product over intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 14 (1), 12–19. Atanassov, K. (2012). On Intuitionistic Fuzzy Sets Theory, Springer, Berlin. Atanassov, K. (2017). Intuitionistic Fuzzy Logics. Springer, Cham. Atanassov, K., Angelova, N., Szmidt, E., & Kacprzyk, J. (2016). Properties of the intuitionistic fuzzy implication →186. Notes on Intuitionistic Fuzzy Sets, 22 (4), 6–12. Atanassov, K., Ribagin, S., Doukovska, L., & Atanassova, V. (2017). Issue:Intuitionistic fuzzy implication →190. Notes on Intuitionistic Fuzzy Sets, 23 (4), 79–83. 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. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2017). Issue:Intuitionistic fuzzy implication →188. Notes on Intuitionistic Fuzzy Sets, 23 (1), 6–13. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2017). Issue:Intuitionistic fuzzy implication →187. Notes on Intuitionistic Fuzzy Sets, 23 (2), 37–43. Atanassov, K., Szmidt, E., & Angelova, N. (2017). Properties of the intuitionistic fuzzy implication →187. Notes on Intuitionistic Fuzzy Sets, 23 (3), 3–8. Atanassova, L. (2017). Issue:Intuitionistic fuzzy implication →189. Notes on Intuitionistic Fuzzy Sets, 23 (1), 14–20. Mendelson, E. (1964). Introduction to Mathematical Logic, Princeton, NJ: D. Van Nostrand. Vassilev, P., Ribagin, S., & Kacprzyk, J. (2018) A remark on intuitionistic fuzzy implications. Notes on Intuitionistic Fuzzy Sets, 24 (2), 1–7. Citations: Issue:Intuitionistic fuzzy interpretations of formula (A → B) → ((¬A → B) → B) ‎ (← links) The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.