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Isotone fuzzy Galois connections with hedges. (English) Zbl 1226.06001

Summary: We study isotone fuzzy Galois connections and concept lattices parameterized by particular unary operators. The operators represent linguistic hedges such as “very”, “rather”, “more or less”, etc. Isotone fuzzy Galois connections and concept lattices provide an alternative to their antitone counterparts which are the fundamental structures behind formal concept analysis of data with fuzzy attributes. We show that hedges enable us to control the number of formal concepts in the associated concept lattice. We also describe the structure of the concept lattice and provide a counterpoint to the main theorem of concept lattices.

MSC:

06A15 Galois correspondences, closure operators (in relation to ordered sets)
06B99 Lattices
68T30 Knowledge representation
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