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 krat@bas.bg Nora Angelova Institute of Biophysics and Biomedical Engineerin, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl. 105, 1113 Sofia, Bulgaria nora.angelova@biomed.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 Download:  PDF (133  Kb, File info) 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: 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. Atanassov, K. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg. Atanassov, K. (2012) On Intuitionistic Fuzzy Sets Theory. Springer, Berlin. 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. Atanassov, K. (2015) Intuitionistic fuzzy logics as tools for evaluation of Data Mining processes, Knowledge-Based Systems, 80, 122–130. Atanassov, K. (2016) On intuitionistic fuzzy implications, Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 12 (in press). 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). Van Atten, M. (2004) On Brouwer, Wadsworth, Behnout. Baczynski, M., & Jayaram, B. (2008) Fuzzy Implications, Springer, Berlin. Brouwer, L.E.J. (1975) Collected Works, Vol. 1, North Holland, Amsterdam. Van Dalen, D. (Ed.) (1981) Brouwer’s Cambridge Lectures on Intuitionism, Cambridge Univ. Press, Cambridge. Mendelson, E. (1964) Introduction to Mathematical Logic, Princeton, NJ: D. Van Nostrand. Plisko, V. (2009) A survey of propositional realizability logic. The Bulletin of Symbolic Logic, 15(1), 1–42. Rose, G.F. (1953) Propositional calculus and realizability. Transactions of the American Mathematical Society, 75, 1–19. Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.