As of August 2024, International Journal "Notes on Intuitionistic Fuzzy Sets" is being indexed in Scopus.
Please check our Instructions to Authors and send your manuscripts to nifs.journal@gmail.com. Next issue: March 2025.

Issue:On the representation of intuitionistic fuzzy t-norms and t-conorms

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Jump to navigation Jump to search
shortcut
http://ifigenia.org/wiki/issue:nifs/8/3/1-10
Title of paper: On the representation of intuitionistic fuzzy t-norms and t-conorms
Author(s):
Glad Deschrijver
Department of Mathematics and Computer Science, Ghent University, Fuzziness and Uncertainty Modelling Research Unit, Krijgslaan 281 (S9), B-9000 Gent, Belgium
glad.deschrijver@rug.ac.be
Chris Cornelis
Department of Mathematics and Computer Science, Ghent University, Fuzziness and Uncertainty Modelling Research Unit, Krijgslaan 281 (S9), B-9000 Gent, Belgium
chris.cornelis@rug.ac.be
Etienne E. Kerre
Department of Mathematics and Computer Science, Ghent University, Fuzziness and Uncertainty Modelling Research Unit, Krijgslaan 281 (S9), B-9000 Gent, Belgium
etienne.kerre@rug.ac.be
Presented at: 6th ICIFS, Varna, 13—14 Sept 2002
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 8 (2002) Number 3, pages 11—25
Download:  PDF (1008  Kb, File info)
Abstract: In fuzzy set theory, an important class of triangular norms and conorms is the class of continuous Archimedean nilpotent triangular norms and conorms. It has been shown that for such t-norms T there exists a bijection φ on [0, 1] such that T is the φ-transform of the Lukasiewicz t-norm. From this class of t-norms an important class of fuzzy implicators can be generated : the class of Lukasiewicz implicators. In this paper we introduce the notion of intuitionistic fuzzy t-norm and t-conorm, and investigate under which conditions a similar representation theorem can be obtained. We also establish a representation theorem for intuitionistic fuzzy Lukasiewicz implicators.
Keywords: intuitionistic fuzzy set, intuitionistic fuzzy triangular norm and conorm, representation theorem, archimedean property, nilpotency, φ-transform
References:
  1. K. T. Atanassov, Intuitionistic fuzzy sets, 1983, VII ITKR’s Session, Sofia (deposed in Central Sci.-Technical Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian).
  2. K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87-96.
  3. K. T. Atanassov, Intuitionistic fuzzy sets, Physica-Verlag, Heidelberg/New York, 1999.
  4. H. Bustince, J. Kacprzyk and V. Mohedano, Intuitionistic fuzzy generators - Application to intuitionistic fuzzy complementation, Fuzzy Sets and Systems 114 (2000), 485-504.
  5. C. Cornelis and G. Deschrijver, The compositional rule of inference in an intuitionistic fuzzy logic setting, In Proceedings of the ESSLLI 2001 Student Session (K. Striegnitz, Ed.), 2001, pp. 83-94.
  6. C. Cornelis, G. Deschrijver, M. De Cock and E. E. Kerre, Intuitionistic fuzzy relational calculus: an overview, 2002, Accepted to IS’02.
  7. C. Cornelis, G. Deschrijver and E. E. Kerre, Classification of intuitionistic fuzzy implicators: an algebraic approach, In Proceedings of the 6th Joint Conference on Information Sciences (H. J. Caulfield, S. Chen, H. Chen, R. Duro, V. Honaver, E. E. Kerre, M. Lu, M. G. Romay, T. K. Shih, D. Ventura, P. P. Wang and Y. Yang, Eds.), 2002, pp. 105-108.
  8. C. Cornelis and E. E. Kerre, Reliability of information: motivation for an intuitionistic theory of possibility, 2001, Submitted to Fuzzy Sets and Systems.
  9. C. Cornelis and E. E. Kerre, On the structure and interpretation of an intuitionistic fuzzy expert system, 2002, Submitted to Eurofuse’02.
  10. C. Cornelis, G. Deschrijver and E. E. Kerre, Implication in Intuitionistic and Interval—Valued Fuzzy Set Theory: Construction, Classification, Application, 2002, Submitted to International Journal of Approximate Reasoning.
  11. G. Deschrijver, C. Cornelis and E. E. Kerre, Intuitionistic Fuzzy Connectives Revisited, 2002, Accepted to IPMU.
  12. G. Deschrijver, C. Cornelis and E. E. Kerre, On the representation of intuitionistic fuzzy t-norms and t-conorms, submitted to Fuzzy Sets and Systems.
  13. G.Deschrijver and E. E. Kerre, On the relationship between some extensions of fuzzy theory, Accepted to Fuzzy Sets and Systems.
  14. D. Dubois and H. Prade, Fuzzy logics and generalized modus ponens revised, Int. J. Cybernetics and Systems 15 (1984), 293-331.
  15. J. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 18 (1967), 145-174.
  16. E. Hewitt and K. Stromberg, Real and abstract analysis, Springer-Verlag, Berlin Heidelberg New York, 1965.
  17. E. P. Klement, R. Mesiar and E. Pap, Triangular norms, Kluwer Academic Publishers, Dordrecht, 2002.
  18. H. Sagan, Advanced calculus, Houghton Mifflin Company, Boston, 1974.
  19. P. Smets and P. Magrez, Implication in fuzzy logic, International Journal of Approximate Reasoning 1 (1987), 327-347.
  20. E. Szmidt and J. Kacprzyk, Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems 114 (2000), 505-518.
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.

Retrieved from "https://ifigenia.org/index.php?title=Issue:On_the_representation_of_intuitionistic_fuzzy_t-norms_and_t-conorms&oldid=13074"