Title of paper:
|
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
|
Department of Economy, 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 28 (2022), Number 1, pages 1–10
|
DOI:
|
https://doi.org/10.7546/nifs.2022.28.1.1-10
|
Download:
|
PDF (892 Kb, File info)
|
Abstract:
|
In this paper, a new weak intuitionistic fuzzy implication is introduced based on the recently defined △* operation. Fulfillment of some axioms and properties, together with Modus Ponens and Modus Tollens inference rules, are investigated. The negation induced by the studied implication is presented.
|
Keywords:
|
Intuitionistic fuzzy implication, Intuitionistic fuzzy logic.
|
AMS Classification:
|
03B52, 03E72
|
References:
|
- Atanassov, K. T., (1983). Intuitionistic fuzzy sets (1983). VII ITKR’s Sci. Session, Sofia, (June 1983) (Deposed in Central Sci. – Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprint and English version in: International Journal Bioautomation, 2016, 20(Suppl. 1), 1–6.
- Atanassov, K.T. (2017). Intuitionistic Fuzzy Logics. Springer. Cham.
- Atanassov, K.T. (2021). Third Zadeh’s intuitionistic fuzzy implication. Mathematics, 9(6), Article 619.
- Atanassov, K. T., Angelova, N., & Atanassova, V. (2021). On an intuitionistic fuzzy form of the Goguen's implication. Mathematics, 9(6), Article 676.
- Atanassov, K. T., Szmidt, E., & Kacprzyk, J. (2013). On intuitionistic fuzzy pairs. Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13.
- Atanassova, L. (2009). A new intuitionistic fuzzy implication. Cybernetics and Information Technologies, 9(2), 21–25.
- Atanassova, L. (2012). On two modifications of the intuitionistic fuzzy implication →@. Notes on Intuitionistic Fuzzy Sets, 18(2), 26–30.
- Atanassova, L. (2013). On the modal form of the intuitionistic fuzzy implications →'@ and →@. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 10, 5–11
- Atanassova, L. (2015). Remark on Dworniczak’s intuitionistic fuzzy implications. Part 1. Notes on Intuitionistic Fuzzy Sets, 21(3), 18–23.
- Atanassova, L. (2016). Remark on Dworniczak’s Intuitionistic Fuzzy Implications. Part 2. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 12, 61–67.
- Atanassova, L. (2016). Remark on Dworniczak's intuitionistic fuzzy implications. Part 3. Notes on Intuitionistic Fuzzy Sets, 22(1), 1–6.
- Atanassova, L. (2020). A new operator over intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 26(1), 23–28.
- Atanassova, L., & Dworniczak, P. (2021). On the operation △ over intuitionistic fuzzy sets. Mathematics, 9(13), Article 1518.
- Atanassova, L., & Dworniczak, P. (2021). On the weak intuitionistic fuzzy implication based on △ operation. Notes on Intuitionistic Fuzzy Sets, 27(2), 11–19.
- Baczyński, M., & Jayaram, B. (2008). Fuzzy Implications. Springer: Berlin.
- 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.
- Cornelis, C., Deschrijver, G., Cock, M., & Kerre, E. E. (2002). Intuitionistic fuzzy relational calculus. Proceedings of the First International IEEE Symposium “Intelligent Systems”, Vol. 1, September 10–12, 2002, Varna, Bulgaria, 340–345.
- 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.
- 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, 35(1), 55–95.
- Dworniczak, P. (2010). On one class of intuitionistic fuzzy implications. Cybernetics and Information Technologies, 10(4), 13–21.
- Dworniczak, P. (2010). Some remarks about the L. Atanassova’s paper “A new intuitionistic fuzzy implication”. Cybernetics and Information Technologies, 10(3), 3–9.
- Dworniczak, P. (2011). Inclusion of the intuitionistic fuzzy sets based on some weak intuitionistic fuzzy implications. Cybernetics and Information Technologies, 11(3), 12–22.
- Dworniczak, P. (2011). On some two-parametric intuitionistic fuzzy implications. Notes on Intuitionistic Fuzzy Sets, 17(2), 8–16.
- Dworniczak, P. (2021). On a new operation over intuitionistic fuzzy sets. Comptes rendus de l'Académie bulgare des Sciences, 75(3), 331–339.
- 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, 157(24), 3231–3236.
- Wang, Z., Xu, Z., Liu, S., & Yao, Z. (2014). Direct clustering analysis based on intuitionistic fuzzy implication. Applied Soft Computing, 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, 179(7), 883–898.
|
Citations:
|
The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.
|
|