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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, 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:
  1. Andonov, V. (2008). On some properties of one Cartesian product over intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 14 (1), 12–19.
  2. Atanassov, K. (2012). On Intuitionistic Fuzzy Sets Theory, Springer, Berlin.
  3. Atanassov, K. (2017). Intuitionistic Fuzzy Logics. Springer, Cham.
  4. 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.
  5. Atanassov, K., Ribagin, S., Doukovska, L., & Atanassova, V. (2017). Issue:Intuitionistic fuzzy implication →190. Notes on Intuitionistic Fuzzy Sets, 23 (4), 79–83.
  6. 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.
  7. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2017). Issue:Intuitionistic fuzzy implication →188. Notes on Intuitionistic Fuzzy Sets, 23 (1), 6–13.
  8. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2017). Issue:Intuitionistic fuzzy implication →187. Notes on Intuitionistic Fuzzy Sets, 23 (2), 37–43.
  9. Atanassov, K., Szmidt, E., & Angelova, N. (2017). Properties of the intuitionistic fuzzy implication →187. Notes on Intuitionistic Fuzzy Sets, 23 (3), 3–8.
  10. Atanassova, L. (2017). Issue:Intuitionistic fuzzy implication →189. Notes on Intuitionistic Fuzzy Sets, 23 (1), 14–20.
  11. Mendelson, E. (1964). Introduction to Mathematical Logic, Princeton, NJ: D. Van Nostrand.
  12. 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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