16-17 May 2019 • Sofia, Bulgaria

Submission: 1 February 2019 • Notification: 1 March 2019 • Final Version: 1 April 2019

Issue:New Fodor's type of intuitionistic fuzzy implication and negation

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Title of paper: New Fodor’s type of intuitionistic fuzzy implication and negation
Author(s):
Krassimir Atanassov
Bioinformatics and Mathematical Modelling Department, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria
Intelligent Systems Laboratory, Prof. Asen Zlatarov University, Bourgas–8000, Bulgaria
kratAt sign.pngbas.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
szmidtAt sign.pngibspan.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
kacprzykAt sign.pngibspan.waw.pl


Presented at: 20th International Conference on Intuitionistic Fuzzy Sets, 2–3 September 2016, Sofia, Bulgaria
Published in: "Notes on IFS", Volume 22, 2016, Number 3, pages 1—8
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Abstract: A new Fodor’s type of intuitionistic fuzzy implication is constructed. Its relation with some forms of Klir and Yuan’s axioms, of intuitionistic logoc axioms, of Kolmogorov’s axioms and of Łukasiewicz-Tarski’s axioms are studied.
Keywords: Implication, Intuitionistic fuzzy logic, Intuitionistic logic, Negation.
AMS Classification: 03E72.
References:
  1. Atanassov, K. (1988) Two Variants of Intuitionistic Fuzzy Propositional Calculus, Mathematical Foundations of Artificial Intelligence Seminar, Sofia, 1988, Preprint IM-MFAIS-5-88. Reprinted: Int J Bioautomation, 2016, 20(S1), S17–S26.
  2. Atanassov, K. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg.
  3. Atanassov, K. (2006) On the implications and negations over intuitionistic fuzzy sets. Proceedings of the Scientific Conference of Burgas Free University, Burgas, 9–11 June 2006, Vol. III, 374–384.
  4. Atanassov, K. (2012) On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
  5. Atanassov, K. (2016) On intuitionistic fuzzy implications, Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 12 (in press).
  6. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2013) On intuitionistic fuzzy pairs, Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13.
  7. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2015) On Fodor’s type of intuitionistic fuzzy implication and negation, Notes on Intuitionistic Fuzzy Sets, 21(2), 25–34.
  8. Baczynski, M., & Jayaram, B. (2008) Fuzzy Implications, Springer, Berlin.
  9. Klir, G. & Yuan, B. (1995) Fuzzy Sets and Fuzzy Logic. Prentice Hall, New Jersey.
  10. Rasiovam H., & Sikorski R. (1963) The mathematics of Metamathematics, Polish Academy of Sciences, Warszawa.
  11. Van Stigtm W. P. (1990) Brouwer’s Intuitionism, North-Holland, Amsterdam.
  12. Szmidt, E., Kacprzyk, J., & Atanassov, K. (2015) Properties of Fodor’s intuitionistic fuzzy implication and negation. Notes on Intuitionistic Fuzzy Sets, 21(4), 6–12.
  13. Szmidt, E., Kacprzyk, J., & Atanassov, K. (2015) Modal forms of Fodor’s type of intuitionistic fuzzy implication. Notes on Intuitionistic Fuzzy Sets, 21(5), 1–5.
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