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  1. Non-dual fuzzy connections.George Georgescu & Andrei Popescu - 2004 - Archive for Mathematical Logic 43 (8):1009-1039.
    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 (...)
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  • Fuzzy Galois Connections.Radim Bêlohlávek - 1999 - Mathematical Logic Quarterly 45 (4):497-504.
    The concept of Galois connection between power sets is generalized from the point of view of fuzzy logic. Studied is the case where the structure of truth values forms a complete residuated lattice. It is proved that fuzzy Galois connections are in one-to-one correspondence with binary fuzzy relations. A representation of fuzzy Galois connections by Galois connections is provided.
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  • Concept lattices and order in fuzzy logic.Radim Bĕlohlávek - 2004 - Annals of Pure and Applied Logic 128 (1-3):277-298.
    The theory of concept lattices is approached from the point of view of fuzzy logic. The notions of partial order, lattice order, and formal concept are generalized for fuzzy setting. Presented is a theorem characterizing the hierarchical structure of formal fuzzy concepts arising in a given formal fuzzy context. Also, as an application of the present approach, Dedekind–MacNeille completion of a partial fuzzy order is described. The approach and results provide foundations for formal concept analysis of vague data—the propositions “object (...)
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  • Lattices of Fixed Points of Fuzzy Galois Connections.Radim Bělohlávek - 2001 - Mathematical Logic Quarterly 47 (1):111-116.
    We give a characterization of the fixed points and of the lattices of fixed points of fuzzy Galois connections. It is shown that fixed points are naturally interpreted as concepts in the sense of traditional logic.
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