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

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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.angelovaAt sign.pngbiomed.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.marinovAt sign.pnggmail.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
kratAt sign.pngbas.bg


Published in: "Notes on IFS", Volume 21, 2015, Number 2, pages 35—42
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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:
  1. Atanassov, K. (2012) On Intuitionistic Fuzzy Sets Theory, Springer, Berlin.
  2. 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.
  3. Atanassov, K. (2015) On a new intuitionistic fuzzy implication. Proc. of IFSA-EUSFLAT 2015 (accepted).
  4. Dimitrov, D. (2011) IFSTool – Software for intuitionistic fuzzy sets. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 9, 61–69.
  5. Tabakov, M. (1986) Logics and axiomatics, Nauka i Izkustvo, Sofia.
  6. Implications over intuitionistic fuzzy sets. Ifigenia.net. Available at: http://www.ifigenia.org/wiki/IF_implications
  7. Negations over intuitionistic fuzzy sets. Ifigenia.net. Available at: http://www.ifigenia.org/wiki/IF_negations
  8. IFSTool. Ifigenia.net. Available at: http://www.ifigenia.org/wiki/IFSTool
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