A characterization theorem for t-representable n-dimensional triangular norms

Bedregal, B., Beliakov, G., Bustince, H., Calvo, T., Fernandez, J. and Mesiar, R. 2011, A characterization theorem for t-representable n-dimensional triangular norms. In Melo-Pinto, Pedro, Serodio, Carlos, Couto, Pedro, Fodor, Janos and De Baets, Bernard (ed), Eurofuse 2011 : workshop on fuzzy methods for knowlege-based systems, Springer - Verlag, Berlin, Germany, pp.103-112, doi: 10.1007/978-3-642-24001-0_11.

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Title A characterization theorem for t-representable n-dimensional triangular norms
Author(s) Bedregal, B.
Beliakov, G.ORCID iD for Beliakov, G. orcid.org/0000-0002-9841-5292
Bustince, H.
Calvo, T.
Fernandez, J.
Mesiar, R.
Title of book Eurofuse 2011 : workshop on fuzzy methods for knowlege-based systems
Editor(s) Melo-Pinto, Pedro
Serodio, Carlos
Couto, Pedro
Fodor, Janos
De Baets, Bernard
Publication date 2011
Series Advances in intelligent and soft computing ; 107
Chapter number 11
Total chapters 37
Start page 103
End page 112
Total pages 10
Publisher Springer - Verlag
Place of Publication Berlin, Germany
Keyword(s) fuzzy set
expert system
triangular norm
Summary n-dimensional fuzzy sets are an extension of fuzzy sets that includes interval-valued fuzzy sets and interval-valued Atanassov intuitionistic fuzzy sets. The membership values of n-dimensional fuzzy sets are n-tuples of real numbers in the unit interval [0,1], called n-dimensional intervals, ordered in increasing order. The main idea in n-dimensional fuzzy sets is to consider several uncertainty levels in the memberships degrees. Triangular norms have played an important role in fuzzy sets theory, in the narrow as in the broad sense. So it is reasonable to extend this fundamental notion for n-dimensional intervals. In interval-valued fuzzy theory, interval-valued t-norms are related with t-norms via the notion of t-representability. A characterization of t-representable interval-valued t-norms is given in term of inclusion monotonicity. In this paper we generalize the notion of t-representability for n-dimensional t-norms and provide a characterization theorem for that class of n-dimensional t-norms. © 2011 Springer-Verlag Berlin Heidelberg.
Notes Version of paper originally presented at 'Eurofuse 2011 : workshop on fuzzy methods for knowledge-based systems', Régua, Portugal, 21-23 September.
ISBN 9783642240003
ISSN 1867-5662
Language eng
DOI 10.1007/978-3-642-24001-0_11
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective 970108 Expanding Knowledge in the Information and Computing Sciences
HERDC Research category B1 Book chapter
Copyright notice ©2011, Springer-Verlag
Persistent URL http://hdl.handle.net/10536/DRO/DU:30043126

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