Issue:Intuitionistic fuzzy implications and Kolmogorov’s and Lukasiewisz–Tarski’s axioms of logic

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http://ifigenia.org/wiki/issue:nifs/21/2/35-42

Title of paper: Intuitionistic fuzzy implications and Kolmogorov’s and Lukasiewisz–Tarski’s axioms of logic Author(s): Nora Angelova Bioinformatics and Mathematical Modelling Department, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria nora.angelova@biomed.bas.bg Evgeniy Marinov Bioinformatics and Mathematical Modelling Department, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria evgeni.marinov@gmail.com Krassimir Atanassov Bioinformatics and Mathematical Modelling Department, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., Sofia 1113, Bulgaria krat@bas.bg Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 21, 2015, Number 2, pages 35—42 Download:  PDF (127  Kb, File info) Abstract: During years of research, there have been defined intuitionistic fuzzy implications. In the paper, it is checked which of the basic 149 implications satisfy which Kolmogorov’s and which Lukasiewisz–Tarski’s axioms of logic, whether as (classical) tautologies or as intuitionistic fuzzy tautologies. Keywords: Implication, Intuitionistic fuzzy logic, Kolmogorov’s axioms, Lukasiewisz–Tarski’s axioms. AMS Classification: 03E72. References: Atanassov, K. (2012) On Intuitionistic Fuzzy Sets Theory, Springer, Berlin. Atanassov, K. (2014) On Intuitionistic Fuzzy Logics: Results and Problems. In: Modern Approaches in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, Volume 1: Foundations. (Atanassov, K., M. Baczynski, J. Drewniak, J. Kacprzyk, M. Krawczak, E. Szmidt, M. Wygralak, S. Zadrozny, eds.), SRI-PAS, Warsaw, pages 23–49. Atanassov, K. (2015) On a new intuitionistic fuzzy implication. Proc. of IFSA-EUSFLAT 2015 (accepted). Dimitrov, D. (2011) IFSTool – Software for intuitionistic fuzzy sets. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 9, 61–69. Tabakov, M. (1986) Logics and axiomatics, Nauka i Izkustvo, Sofia. Implications over intuitionistic fuzzy sets. Ifigenia.net. Available at: http://www.ifigenia.org/wiki/IF_implications Negations over intuitionistic fuzzy sets. Ifigenia.net. Available at: http://www.ifigenia.org/wiki/IF_negations IFSTool. Ifigenia.net. Available at: http://www.ifigenia.org/wiki/IFSTool Citations: Issue:Remark on Dworniczak’s intuitionistic fuzzy implications. Part 1 ‎ (← 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.