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

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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: Conference proceedings, "Notes on IFS", 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
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