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Issue:On Intuitionistic Fuzzy Implications

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Title of paper: On Intuitionistic Fuzzy Implications
Author(s):
Krassimir Atanassov
Dept. of Bioinformatics and Mathematical Modelling, 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, Burgas–8010, Bulgaria
krat@bas.bg
Published in: "Issues in IFS and GNs", Volume 12 (2015/2016), pages 1-19
Download:  PDF (170  Kb, File info)
Abstract: The list of all intuitionistic fuzzy implications, introduced by the moment is given. Some properties of these implications are studied.
Keywords: Intuitionistic fuzzy set, Intuitionistic fuzzy implication.
References:
  1. Angelova, N., K. Atanassov. Intuitionistic Fuzzy Implications and the Axioms of Intuitionistic Logic. 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), 30.06-03.07.2015, Gijon, Spain, 1578–1584.
  2. Angelova, N., K. Atanassov. Intuitionistic Fuzzy Implications and Klir–Yuan’s Axioms. Novel Developments in Uncertainty Representation and Processing. Advances in Intuitionistic Fuzzy Sets and Generalized Nets, Vol. 401 (Atanassov, K.T., Castillo, O., Kacprzyk, J., Krawczak, M., Melin, P., Sotirov, S., Sotirova, E., Szmidt, E., De Tr, G., Zadrony, S., Eds.), 2016, 97–110.
  3. Angelova, N., E. Marinov, K. Atanassov, Intuitionistic fuzzy implications and Kolmogorov’s and Łukasiewisz–Tarski’s axioms of logic. Notes on Intuitionistic Fuzzy Sets, Vol. 21, 2015, No. 2, 35–42.
  4. Atanassov, K. On some intuitionistic fuzzy negations. Notes on Intuitionistic Fuzzy Sets, Vol. 11, 2005, No. 6, 13–20.
  5. Atanassov, K. On some intuitionistic fuzzy implications. Comptes Rendus de l’Academie bulgare des Sciences, Tome 59, 2006, No. 1, 19–24.
  6. Atanassov, K., On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012.
  7. Atanassov, K. A new intuitionistic fuzzy implication from a modal type. Advanced Studies on Contemporary Mathematics, Vol. 12, 2006, No. 1, 117–122.
  8. Atanassov, K. On eight new intuitionistic fuzzy implications. Proc. of 2006 IEEE International Conference on Intelligent Systems, London, 4-6 Sept. 2006, 741–746.
  9. Atanassov, K. On intuitionistic fuzzy implication →ε and intuitionistic fuzzy negation ¬ε. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, Vol. 6, 2008, 6–19.
  10. Atanassov, K. Intuitionistic fuzzy implication →εη and intuitionistic fuzzy negation ¬εη. Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, Vol. 1, 2008, 1–10.
  11. Atanassov, K., On intuitionistic fuzzy negations and Law of Excluded Middle, Proc. of 2010 IEEE International Conference on Intelligent Systems, London, 7-9 July 2010, 266–269.
  12. Atanassov, K. On a New Intuitionistic Fuzzy Implication. Proc. of 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), 30.06-03.07.2015, Gijon, Spain, 1592–1597.
  13. Atanassov, K., B. Kolev. On an intuitionistic fuzzy implication from a probabilistic type. Advanced Studies on Contemporary Mathematics, Vol. 12, 2006, No. 1, 111–116.
  14. Atanassov, K., T. Trifonov. On a new intuitionistic fuzzy implication of Godel’s type. Proceedings of the Jangjeon Mathematical Society, Vol. 8, 2005, No. 2, 147–152.
  15. Atanassov, K., T. Trifonov. Two new intuitionistic fuzzy implications. Advanced Studies on Contemporary Mathematics, Vol. 13, 2006, No. 1, 69–74.
  16. Atanassova, L. A new intuitionistic fuzzy implication, Cybernetics and Information Technologies, Vol. 9, 2009, No. 2, 21–25.
  17. Atanassova, L., On some properties of intuitionistic fuzzy negation →@, Notes on Intuitionistic Fuzzy Sets, Vol. 15, 2009, No. 1, 32–35.
  18. Atanassova, L. On two modifications of the intuitionistic fuzzy implication →@, Notes on Intuitionistic Fuzzy Sets, Vol. 18, 2012, No. 2, 26–30.
  19. Atanassova, L., On the modal form of the intuitionistic fuzzy implications →'@ and →@, Issues in Intuitionistic Fuzzy Sets and Generalized Nets, Vol. 10, 2013, 5–11.
  20. Atanassova, L., Remark on Dworniczak’s intuitionistic fuzzy implications. Part 1, Notes on Intuitionistic Fuzzy Sets, Vol. 21, 2015, No. 3, 18–23.
  21. Atanassova, L. 2015 Remark on Dworniczak’s intuitionistic fuzzy implications. Part 2, Annual of “Informatics” Section Union of Scientists in Bulgaria, Vol. 8, 2015 (in press).
  22. Atanassova, L., Remark on Dworniczak’s intuitionistic fuzzy implications. Part 3, Issues in Intuitionistic Fuzzy Sets and Generalized Nets, Vol. 12, 2015/2016, 61–67.
  23. Dworniczak, P. Some remarks about the L. Atanassova’s paper “A new intuitionistic fuzzy implication”, Cybernetics and Information Technologies, Vol. 10, 2010, 3, 3–9.
  24. Dworniczak, P. On one class of intuitionistic fuzzy implications, Cybernetics and Information Technologies, Vol. 10, 2010, 4, 13–21.
  25. Dworniczak, P. On some two-parametric intuitionistic fuzzy implication, Notes on Intuitionistic Fuzzy Sets, Vol. 17, 2011, No. 2, 8–16.
  26. Klir, G., B. Yuan, Fuzzy Sets and Fuzzy Logic. Prentice Hall, New Jersey, 1995.
  27. Mendelson, E. Introduction to Mathematical Logic, Princeton, NJ: D. Van Nostrand, 1964.
  28. Zadeh, L. Fuzzy logic, IEEE Computer, Vol. 21, No. 4, 1988, 83–93.
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