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(S,N)-implications on bounded lattices
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posted on 2013-01-01, 00:00 authored by B Bedregal, Gleb BeliakovGleb Beliakov, H Bustince, J Fernandez, A Pradera, R ReiserSince the birth of the fuzzy sets theory several extensions have been proposed. For these extensions, different sets of membership functions were considered. Since fuzzy connectives, such as conjunctions, negations and implications, play an important role in the theory and applications of fuzzy logics, these connectives have also been extended. An extension of fuzzy logic, which generalizes the ones considered up to the present, was proposed by Joseph Goguen in 1967. In this extension, the membership values are drawn from arbitrary bounded lattices. The simplest and best studied class of fuzzy implications is the class of (S,N)-implications, and in this chapter we provide an extension of (S,N)-implications in the context of bounded lattice valued fuzzy logic, and we show that several properties of this class are preserved in this more general framework.
History
Title of book
Advances in fuzzy implication functionsSeries
Studies in fuzziness and soft computing ; 300Chapter number
5Pagination
101 - 124Publisher
SpringerPlace of publication
Heidelberg, GermanyPublisher DOI
ISSN
1434-9922ISBN-13
9783642356773ISBN-10
364235677XLanguage
engPublication classification
B1 Book chapterCopyright notice
2013, SpringerExtent
8Editor/Contributor(s)
M Baczynski, G Beliakov, H BustinceSola, A PraderaUsage metrics
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