Archive for Mathematical Logic 43 (8):1009-1039 (2004)

Authors
Andrei Popescu
Politehnica University of Bucharest
Abstract
The lack of double negation and de Morgan properties makes fuzzy logic unsymmetrical. This is the reason why fuzzy versions of notions like closure operator or Galois connection deserve attention for both antiotone and isotone cases, these two cases not being dual. This paper offers them attention, comming to the following conclusions: – some kind of hardly describable ‘‘local preduality’’ still makes possible important parallel results; – interesting new concepts besides antitone and isotone ones (like, for instance, conjugated pair), that were classically reducible to the first, gain independency in fuzzy setting
Keywords Duality  Isotone structure  Fuzzy set theory  Galois connection  conjugated pair  Closure operator
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DOI 10.1007/s00153-004-0240-4
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References found in this work BETA

The Logic of Inexact Concepts.J. A. Goguen - 1969 - Synthese 19 (3-4):325-373.
Lattice Theory.Garrett Birkhoff - 1940 - Journal of Symbolic Logic 5 (4):155-157.
Mathematics Behind Fuzzy Logic.Esko Turunen - 1999 - Physica-Verlag Heidelberg.
Fuzzy Galois Connections.Radim Bêlohlávek - 1999 - Mathematical Logic Quarterly 45 (4):497-504.
Metamathematics of Fuzzy Logic.P. Hájek - 2002 - Studia Logica 72 (3):433-437.

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Citations of this work BETA

Fuzzy Galois Connections on Fuzzy Posets.Wei Yao & Ling-Xia Lu - 2009 - Mathematical Logic Quarterly 55 (1):105-112.
Fuzzy Closure Systems on L-Ordered Sets.Lankun Guo, Guo-Qiang Zhang & Qingguo Li - 2011 - Mathematical Logic Quarterly 57 (3):281-291.

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