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A characterization theorem for t-representable n-dimensional triangular norms
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posted on 2011-01-01, 00:00 authored by B Bedregal, Gleb BeliakovGleb Beliakov, H Bustince, T Calvo, J Fernandez, R Mesiarn-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.
History
Title of book
Eurofuse 2011 : workshop on fuzzy methods for knowlege-based systemsSeries
Advances in intelligent and soft computing ; 107Chapter number
11Pagination
103 - 112Publisher
Springer - VerlagPlace of publication
Berlin, GermanyPublisher DOI
ISSN
1867-5662ISBN-13
9783642240003ISBN-10
3642240003Language
engNotes
Version of paper originally presented at 'Eurofuse 2011 : workshop on fuzzy methods for knowledge-based systems', Régua, Portugal, 21-23 September.Publication classification
B1 Book chapterCopyright notice
2011, Springer-VerlagExtent
37Editor/Contributor(s)
P Melo-Pinto, C Serodio, P Couto, J Fodor, B De BaetsUsage metrics
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