16-17 May 2019 • Sofia, Bulgaria

Submission: 1 February 2019 • Notification: 1 March 2019 • Final Version: 1 April 2019

Issue:Properties of the intuitionistic fuzzy implications and negations

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Title of paper: Properties of the intuitionistic fuzzy implications and negations
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
Intelligent Systems Laboratory, Prof. Asen Zlatarov University, Bourgas–8000, 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
Presented at: 20th International Conference on Intuitionistic Fuzzy Sets, 2–3 September 2016, Sofia, Bulgaria
Published in: "Notes on IFS", Volume 22, 2016, Number 3, pages 25—33
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Abstract: Some basic properties, are formulated and checked for all the 185 intuitionistic fuzzy implications and all the 53 intuitionistic fuzzy negations. Among these properties are Mederith’s axiom, Rose’s formula, the Law for Contraposition, and others.
Keywords: Implication, Intuitionistic fuzzy logic, Intuitionistic logic, Negation.
AMS Classification: 03E72.
References:
  1. Atanassov, K. (1988) Two variants of intuitionistic fuzzy propositional calculus, Mathematical Foundations of Artificial Intelligence Seminar, Sofia, 1988, Preprint IM-MFAIS-5-88. Reprinted: Int J Bioautomation, 2016, 20(S1), S17–S26.
  2. Atanassov, K. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg.
  3. Atanassov, K. (2012) On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
  4. Atanassov, K. (2014) On Intuitionistic Fuzzy Logics: Results and Problems. 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, 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. (2016) On intuitionistic fuzzy implications, Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 12 (in press).
  7. Atanassov, K., & Angelova, N. (2016) On intuitionistic fuzzy negations, Law for Excluded Middle and De Morgan’s Laws, Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 12 (in press).
  8. Van Atten, M. (2004) On Brouwer, Wadsworth, Behnout.
  9. Baczynski, M., & Jayaram, B. (2008) Fuzzy Implications, Springer, Berlin.
  10. Brouwer, L.E.J. (1975) Collected Works, Vol. 1, North Holland, Amsterdam.
  11. Van Dalen, D. (Ed.) (1981) Brouwer’s Cambridge Lectures on Intuitionism, Cambridge Univ. Press, Cambridge.
  12. Mendelson, E. (1964) Introduction to Mathematical Logic, Princeton, NJ: D. Van Nostrand.
  13. Plisko, V. (2009) A survey of propositional realizability logic. The Bulletin 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.
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