Issue:Properties of the intuitionistic fuzzy implication →186

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Title of paper: Properties of the intuitionistic fuzzy implication →186
Author(s):
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
Nora Angelova
Institute of Biophysics and Biomedical Engineerin, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl. 105, 1113 Sofia, Bulgaria
nora.angelovaAt sign.pngbiomed.bas.bg
Eulalia Szmidt
Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447 Warsaw, Poland
szmidtAt sign.pngibspan.waw.pl
Janusz Kacprzyk
Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447 Warsaw, Poland
kacprzykAt sign.pngibspan.waw.pl
Presented at: 3rd International Intuitionistic Fuzzy Sets Conference, 9 Aug – 1 Sep 2016, Mersin, Turkey
Published in: "Notes on IFS", Volume 22, 2016, Number 4, pages 6—12
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Abstract: In [8], a new Fodor's type of intuitionistic fuzzy implication, numbered as →186, was defined and some of its properties were studied. The present paper is a continuation of the previous one. New interesting properties of implication →186 are formulated and checked.
Keywords: Implication, Intuitionistic fuzzy implication, Intuitionistic fuzzy logic.
AMS Classification: 03E72
References:
  1. Atanassov, K. (1988) Two variants of intuitonistc fuzzy propositional calculus. Preprint IM-MFAIS-5-88, Sofia, 1988.
  2. Atanassov, K. (1999) Intuitionistic Fuzzy Sets. Springer, Heidelberg.
  3. Atanassov, K. (2012) On Intuitionistic Fuzzy Sets. Springer, Berlin.
  4. 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, pp. 23–49.
  5. Atanassov, K. (2015) Intuitionistic fuzzy logics as tools for evaluation of data mining processes, Knowledge-Based Systems, 80, 122–130.
  6. Atanassov, K. (2017) Intuitionistic Fuzzy Logics. Springer Publishing House (in press).
  7. Atanassov, K., E. Szmidt, J. Kacprzyk, On Fodor’s type of intuitionistic fuzzy implication and negation, Notes on Intuitionistic Fuzzy Sets, 21, 2015, No. 2, 25–34.
  8. Atanassov, K., Szmidt, E. & Kacprzyk, J. (2016) New Fodor’s Type of Intuitionistic Fuzzy Implication and Negation, Notes on Intuitionistic Fuzzy Sets, 22(3), 1–8.
  9. van Atten, M. (2004) On Brouwer, Wadsworth, Behnout.
  10. Baczynski, M. & Jayaram, B. (2008) Fuzzy Implications, Springer, Berlin.
  11. Brouwer, L. E. J. (1975) Collected Works, Vol. 1, North Holland, Amsterdam.
  12. van Dalen, D. (Ed.) (1981) Brouwer’s Cambridge Lectures on Intuitionism, Cambridge Univ. Press, Cambridge.
  13. Plisko, V. (2009) A survey of propositional realizability logic. The Bulleting of Symbolic Logic, 15(1), 1–42.
  14. Rose, G. F. (1953) Propositional calculus and realizability. Transactions of the American Mathematical Society, 75, 1–19.
  15. Szmidt, E., Kacprzyk, J. & Atanassov, K. (2015) Properties of Fodor’s intuitionistic fuzzy implication and negation. Notes on Intuitionistic Fuzzy Sets, 21(4), 6–12.
  16. Szmidt, E., Kacprzyk, J. & Atanassov, K. (2015) Modal forms of Fodor’s type of intuitionistic fuzzy implication. Notes on Intuitionistic Fuzzy Sets, 21(5), 1–5.
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