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# Atanassov, K.T. (2021). Third Zadeh’s Intuitionistic Fuzzy Implication. Mathematics, Vol. 9, No. 6, 619.
# Edward Samuel, A., & Narmadhagnanam, R. (2018). Intuitionistic Fuzzy Sets in Medical Diagnosis. International Journal of Mathematical Archive, 9 (1), 1–5.
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# Klir, G., & Yuan, B., (1995). Fuzzy sets and fuzzy logic. Prentice Hall, New Jersey.
# Liu, H.-W., & Wang, G.-J., (2006). A note on implicators based on binary aggregation operators in interval-valued fuzzy set theory. Fuzzy Sets and Systems, Vol. 157, No. 24, 3231–3236.
# Wang, Z., Xu, Z., Liu, S., & Yao, Z. (2014). Direct clustering analysis based on intuitionistic fuzzy implication. Applied Soft Computing, Vol. 23, 1–8.
# Zhou, L., Wu, W.-Z., Zhang, & W.-X., (2009). On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators. Information Sciences, Vol. 179,    No. 7, 883–898.


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Revision as of 17:32, 10 September 2021

shortcut
http://ifigenia.org/wiki/issue:nifs/27/2/11-19
Title of paper: On the weak intuitionistic fuzzy implication based on △ operation
Author(s):
Lilija Atanassova
Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 2, Sofia-1113, Bulgaria
l.c.atanassova@gmail.com
Piotr Dworniczak
The Great Poland University of Social and Economics, ul. Surzyńskich 2, 63-000 Środa Wlkp., Poland
p.dworniczak@wwsse.pl
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 2, pages 11–19
DOI: https://doi.org/10.7546/nifs.2021.27.2.11-19
Download:  PDF (803  Kb, Info)
Abstract: In this paper, a new weak intuitionistic fuzzy implication is introduced. Fulfillment of some axioms and properties, together with the Modus Ponens and Modus Tollens inference rules are investigated. Negation induced by the newly proposed implication is presented.
Keywords: Intuitionistic fuzzy sets, Intuitionistic fuzzy logic, Intuitionistic fuzzy implication.
References:
  1. Atanassov, K.T. (1983/2016). Intuitionistic fuzzy sets. VII ITKR’s Sci. Session, Sofia, (June 1983) (Deposed in Central Sci. – Techn. Library of Bulg. Acad. of Sci., Hπ 1697/84) (in Bulg.). Reprint and English version in: International Journal Bioautomation, Vol. 20, supl. 1, 1–6.
  2. Atanassov, K.T. (2017). Intuitionistic Fuzzy Logics. Springer. Cham.
  3. Atanassov, K.T. (2021). Third Zadeh’s Intuitionistic Fuzzy Implication. Mathematics, Vol. 9, No. 6, 619.
  4. Atanassov, K.T., Angelova, N., & Atanassova, V. (2021). On an Intuitionistic Fuzzy Form of the Goguen’s Implication. Mathematics, Vol. 9, No. 6, 676.
  5. Atanassov, K.T., Szmidt, E., & Kacprzyk, J. (2013). On intuitionistic fuzzy pairs. Notes on Intuitionistic Fuzzy Sets, Vol. 19, No. 3, 1–13.
  6. Atanassova, L. (2009). A new intuitionistic fuzzy implication. Cybernetics and Information Technologies, Vol. 9, No 2, 21–25.
  7. Atanassova, L. (2012). On two modifications of the intuitionistic fuzzy implication →@. Notes on Intuitionistic Fuzzy Sets, Vol. 18, No. 2, 26–30.
  8. Atanassova, L. (2013). On the modal form of the intuitionistic fuzzy implications →'@ and →"@. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, Vol. 10, 5–11.
  9. Atanassova, L. (2015). Remark on Dworniczak’s intuitionistic fuzzy implications. Part 1. Notes on Intuitionistic Fuzzy Sets, Vol. 21, No. 3, 18–23.
  10. Atanassova, L. (2016). Remark on Dworniczak’s intuitionistic fuzzy implications. Part 2. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, Vol. 12, 61–67.
  11. Atanassova, L. (2016). Remark on Dworniczak’s intuitionistic fuzzy implications. Part 3. Notes on Intuitionistic Fuzzy Sets, Vol. 22, No. 31, 1–6.
  12. Atanassova, L. (2020). A new operator over intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, Vol. 24, No. 1, 23–28.
  13. Atanassova, L., & Dworniczak, P. (2021). On the operation △ over intuitionistic fuzzy sets. Mathematics, in print.
  14. Baczyński, M., & Jayaram, B. (2008). Fuzzy implications. Springer, Berlin.
  15. Cornelis, C., & Deschrijver, G. (2001). The compositional rule of inference in an intuitionistic fuzzy logic setting (cited also as: The compositional rule of inference in an intuitionistic fuzzy logic framework). In: Striegnitz, K., (ed.), Proceedings of ESSLLI 2001, Student Session, Kluwer Academic Publishers, 83–94.
  16. Cornelis, C., Deschrijver, G., Cock, M., & Kerre, E.E. (2002). Intuitionistic fuzzy relational calculus. Proceedings of the First International IEEE Symposium “Intelligent Systems”, September 2002, Varna, Vol. 1, 340–345.
  17. Cornelis, C., Deschrijver, G., & Kerre, E.E. (2002). Classification of intuitionistic fuzzy implicators: an algebraic approach. Proceedings of the FT&T’02, 8th International Conference on Fuzzy Theory and Technology, March 9–12, 2002, Durham, North Carolina, USA, 105–108.
  18. Cornelis, C., Deschrijver, G., & Kerre, E.E. (2004). Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application. International Journal of Approximate Reasoning, Vol. 35, No.1, 55–95.
  19. Dworniczak, P. (2011). Inclusion of the intuitionistic fuzzy sets based on some weak intuitionistic fuzzy implications. Cybernetics and Information Technologies, Vol. 11, No. 3, 12–22.
  20. Dworniczak, P. (2010). Some remarks about the L. Atanassova’s paper “A new intuitionistic fuzzy implication”. Cybernetics and Information Technologies, Vol.10, No 3, 3–9.
  21. Dworniczak, P. (2010). On one class of intuitionistic fuzzy implications. Cybernetics and Information Technologies, Vol. 10, No. 4, 13–21.
  22. Dworniczak, P. (2011). On some two-parametric intuitionistic fuzzy implications. Notes on Intuitionistic Fuzzy Sets, Vol. 17, No. 2, 8–16.
  23. Klir, G., & Yuan, B., (1995). Fuzzy sets and fuzzy logic. Prentice Hall, New Jersey.
  24. Liu, H.-W., & Wang, G.-J., (2006). A note on implicators based on binary aggregation operators in interval-valued fuzzy set theory. Fuzzy Sets and Systems, Vol. 157, No. 24, 3231–3236.
  25. Wang, Z., Xu, Z., Liu, S., & Yao, Z. (2014). Direct clustering analysis based on intuitionistic fuzzy implication. Applied Soft Computing, Vol. 23, 1–8.
  26. Zhou, L., Wu, W.-Z., Zhang, & W.-X., (2009). On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators. Information Sciences, Vol. 179, No. 7, 883–898.
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