Issue:Research on intuitionistic fuzzy implications. Part 2

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Title of paper: Research on intuitionistic fuzzy implications. Part 2 Author(s): Nora Angelova Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria noraa@fmi.uni-sofia.bg 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 krat@bas.bg Vassia Atanassova Dept. of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria vassia.atanassova@gmail.com Published in: Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 2, pages 172–192 DOI: https://doi.org/10.7546/nifs.2022.28.2.172-192 Download:  PDF (583  Kb, File info) Abstract: Continuing the research from [2], here we give the list of the axioms that are satisfied by the intuitionistic fuzzy implications, introduced in Part 1 of the present research. Given the large number of implications that have already been defined and the naturally arising question about their comparability and usability, we discuss the criteria of usability of implications and outline 44 ones that satisfy at least 28 from the discussed 38 axioms, that is about 1/4 of all implications that satisfy at least about 3/4 of all axioms. Finally, we show the relationships between each pair of implications in the form of a graph. Keywords: Intuitionistic fuzzy implication, Intuitionistic fuzzy pair, Intuitionistic fuzzy set, Logic axiom. AMS Classification: 03E72. References: Angelova, N. (2021). IFSTOOL - Software for Intuitionistic Fuzzy Sets Necessity, Possibility and Circle Operators. Advances in Intelligent Systems and Computing, Vol. 1081, 76-81, doi:10.1007/978-3-030-47024-1_9 Angelova, N., & Atanassov, K. (2021). Research on intuitionistic fuzzy implications. Notes on Intuitionistic Fuzzy Sets, 27(2), 20-93. Angelova, N., & Atanassov, K. (2021). Research on intuitionistic fuzzy negations. Notes on Intuitionistic Fuzzy Sets, 27(3), 18-31. Atanassov, K. (2017). Intuitionistic Fuzzy Logics. Springer, Cham. Klir, G., & Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic. Prentice Hall, New Jersey. Rasiowa, H., & Sikorski, R. (1963). The Mathematics of Metamathematics. Polish Academy of Sciences, Warsaw. Tabakov, M. (1986). Logics and Axiomatics. Nauka i Izkustvo, Sofia. Citations: Issue:The Hauber's law with intuitionistic fuzzy implications ‎ (← links) Issue:A new intuitionistic fuzzy implication and the negation, conjunctions and disjunctions generated by it ‎ (← links) Issue:Research on intuitionistic fuzzy implications. Part 3 ‎ (← links) Issue:Research on intuitionistic fuzzy implications. Part 4 ‎ (← links) The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.