Notes on Intuitionistic Fuzzy Sets Print ISSN 1310–4926, Online ISSN 2367–8283 Vol. 27, 2021, No. 1, 9–23 DOI: 10.7546/nifs.2020.27.1.9-23 Modifications of the Third Zadeh’s intuitionistic fuzzy implication Krassimir T. Atanassov 1,2 and Nora Angelova 3 1 Dept. of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences 105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria 2 Intelligent Systems Laboratory Prof. Dr. Asen Zlatarov University, 8010 Burgas, Bulgaria e-mail: krat@bas.bg 3 Faculty of Mathematics and Informatics, Sofia University 5 James Bourchier Blvd., 1164 Sofia, Bulgaria e-mail: noraa@fmi.uni-sofia.bg Received: 7 December 2020 Revised: 22 March 2021 Accepted: 28 March 2021 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. 2020 Mathematics Subject Classification: 03E72. 1 Introduction Implication is one of the basic operations in logic, and in intuitionistic fuzzy logic it has become a special object of investigation. Due to its definition, where the second degree – of non-membership, non-validity, etc. – has been introduced, intuitionistic fuzzy sets allow working with not just one, but multiple differently defined intuitionistic fuzzy implications. The extensive research 9