16-17 May 2019 • Sofia, Bulgaria

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

Issue:Modal forms of Fodor's type of intuitionistic fuzzy implication

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Title of paper: Modal forms of Fodor's type of intuitionistic fuzzy implication
Author(s):
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
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
Presented at: 11th International Workshop on Intuitionistic Fuzzy Sets, Banská Bystrica, Slovakia, 30 Oct. 2015
Published in: "Notes on IFS", Volume 21, 2015, Number 5, pages 1–6
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Abstract: Herewith proposed are four new intuitionistic fuzzy implications, based on the Fodor’s type of intuitionistic fuzzy implication, introduced earlier by the authors. These four implications are modifications of the first implication, but in modal forms. Some of their properties are discussed.
Keywords: Implication, Intuitionistic fuzzy logic, Intuitionistic logic, Negation.
AMS Classification: 03E72
References:
  1. Atanassov, K. T. (1988) Two Variants of Intuitionistic Fuzzy Propositional Calculus, Mathematical Foundations of Artificial Intelligence Seminar, Sofia, Preprint IM-MFAIS-5-88. Reprinted: Int. J. Bioautomation, Vol. 19, 2015, Suppl. 2, S146–S155.
  2. Atanassov, K. (2012) On Intuitionistic Fuzzy Sets Theory, Springer, Berlin.
  3. Atanassov, K., E. Szmidt, & J. Kacprzyk (2013) On intuitionistic fuzzy pairs, Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13.
  4. Atanassov, K. (2015) On intuitionistic fuzzy implications. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 12, (in press).
  5. Atanassov, K., E. Szmidt & J. Kacprzyk. (2013) On intuitionistic fuzzy pairs. Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13.
  6. Atanassov, K., E. Szmidt & J. Kacprzyk. (2015) On Fodors type of intuitionistic fuzzy implication and negation. Notes on Intuitionistic Fuzzy Sets, 21(2), 25–34.
  7. Fodor, J. & R. Roubens. (1994) Fuzzy Preference Modelling and Multicriteria Decision Support, Springer.
  8. Rasiova H. & R. Sikorski. (1963) The Mathematics of Metamathematics. Polish Academy of Sciences, Warszawa.
  9. Tabakov, M. (1986) Logics and axiomatics. Nauka i Izkustvo, Sofia (in Bulgarian).
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