(S,N)-implications on bounded lattices

Bedregal, Benjamin, Beliakov, Gleb, Bustince, Humberto, Fernandez, Javier, Pradera, Ana and Reiser, Renata 2013, (S,N)-implications on bounded lattices. In Baczynski, Michal, Beliakov, Gleb, BustinceSola, Humberto and Pradera, Ana (ed), Advances in fuzzy implication functions, Springer, Heidelberg, Germany, pp.101-124, doi: 10.1007/978-3-642-35677-3_5.

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Title (S,N)-implications on bounded lattices
Author(s) Bedregal, Benjamin
Beliakov, GlebORCID iD for Beliakov, Gleb orcid.org/0000-0002-9841-5292
Bustince, Humberto
Fernandez, Javier
Pradera, Ana
Reiser, Renata
Title of book Advances in fuzzy implication functions
Editor(s) Baczynski, Michal
Beliakov, Gleb
BustinceSola, Humberto
Pradera, Ana
Publication date 2013
Series Studies in fuzziness and soft computing ; 300
Chapter number 5
Total chapters 8
Start page 101
End page 124
Total pages 24
Publisher Springer
Place of Publication Heidelberg, Germany
Summary Since 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.
ISBN 364235677X
ISSN 1434-9922
Language eng
DOI 10.1007/978-3-642-35677-3_5
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 ©2013, Springer
Persistent URL http://hdl.handle.net/10536/DRO/DU:30055199

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