Issue:Modifications of the Third Zadeh's intuitionistic fuzzy implication

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Title of paper: Modifications of the Third Zadeh’s intuitionistic fuzzy implication 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., 1113 Sofia, Bulgaria Intelligent Systems Laboratory, Prof. Dr. Asen Zlatarov University, 8010 Burgas, Bulgaria krat@bas.bg Nora Angelova Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria noraa@fmi.uni-sofia.bg Published in: Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 1, pages 9–23 DOI: https://doi.org/10.7546/nifs.2021.27.1.9-23 Download:  PDF (151  Kb, File info) Abstract: In [24], G. Klir and B. Yuan named after L. Zadeh the implication p → q = max(1 − p, min(p, q)). In a series of papers, the author introduced two intuitionistic fuzzy forms of Zadeh’s implication and their basic properties have been studied. In the present paper, a new (third) intuitionistic fuzzy form of Zadeh’s implication is given and some of its properties are studied. Keywords: Intuitionistic fuzzy implication, Intuitionistic fuzzy set, Zadeh’s fuzzy implication. AMS Classification: 03E72 References: Angelova, N., & Stoenchev, M. (2015/2016). Intuitionistic fuzzy conjunctions and disjunctions from first type. Annual of “Informatics” Section, Union of Scientists in Bulgaria, 8, 1–17. Angelova, N., Stoenchev, M., & Todorov, V. (2017). Intuitionistic fuzzy conjunctions and disjunctions from second type. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 13, 143–170. Angelova, N., & Stoenchev, M. (2017). Intuitionistic fuzzy conjunctions and disjunctions from third type. Notes on Intuitionistic Fuzzy Sets, 23(5), 29–41. Atanassov, K. (1999). Intuitionistic Fuzzy Sets: Theory and Applications, Springer, Heidelberg. Atanassov, K. (2006). On some intuitionistic fuzzy implication. Comptes Rendus de l’Academie bulgare des Sciences, 59(1), 21–26. Atanassov, K. (2006). A new intuitionistic fuzzy implication from a modal type. Advanced Studies in Contemporary Mathematics, 12(1), 117–122. Atanassov, K. (2011). Second Zadeh's intuitionistic fuzzy implication. Notes on Intuitionistic Fuzzy Sets, 17(3), 11–14. Atanassov, K. (2012). On Intuitionistic Fuzzy Sets Theory, Springer, Berlin. Atanassov, K. (2017). Intuitionistic Fuzzy Logics, Springer, Cham. Atanassov, K. (2019) On the intuitionistic fuzzy implication →191. Notes on Intuitionistic Fuzzy Sets, 25(4), 1–6. Atanassov, K., Angelova, N., & Atanassova, V. (2021). On an Intuitionistic Fuzzy Form of the Goguen’s Implication. Mathematics 9(6), Article ID 676. Atanassov, K. (2021). Third Zadeh’s Intuitionistic Fuzzy Implication. Mathematics, 9(6), Article ID 619. Atanassova, L. (2009). A new intuitionistic fuzzy implication. Cybernetics and Information Technologies, 9(2), 21–25. Atanassova, L. (2009). On some properties of intuitionistic fuzzy negation ¬@. Notes on Intuitionistic Fuzzy Sets, 15(1), 32–35. 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. (2015/2016). Remark on Dworniczak’s intuitionistic fuzzy implications. Part 2. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 12, 61–67. Chen, J., & Kundu, S. (1996). A sound and complete fuzzy logic system using Zadeh’s implication operator. Lecture Notes in Computer Science, 1079, 233–242. 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. (2010). On one class of intuitionistic fuzzy implications. Cybernetics and Information Technologies, 10(4), 13–21. Dworniczak, P. (2011). On some two-parametric intuitionistic fuzzy implications. Notes on Intuitionistic Fuzzy Sets, 17(2), 8–16. Feys, R. (1965). Modal logics, Gauthier-Villars, Paris. Klir, G., & Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic, Prentice Hall, New Jersey. Mendelson, E. (1964). Introduction to Mathematical Logic, D. Van Nostrand, Princeton, New Jersey. Rasiova, H., & Sikorski, R.(1963). The Mathematics of Metamathematics, Pol. Acad. of Sci., Warszawa. Vassilev, P., & Atanassov, K. (2019). Extensions and Modifications of Intuitionistic Fuzzy Sets, “Prof. Marin Drinov” Academic Publishing House, Sofia. 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.