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A categorical view at generalized concept lattices. (English) Zbl 1132.06300
Summary: We continue in the direction of the ideas from G.-Q. Zhang’s paper [“Chu spaces, concept lattices, and domains”, in: Proc. 19th conference on mathematical foundations of programming semantics, Montreal 2003, Electron. Notes Theor. Comput. Sci. 83 (2004)] about a relationship between Chu spaces and formal concept analysis. We modify this categorical point of view at a classical concept lattice to a generalized concept lattice (in the sense of [S. Krajči, “A generalized concept lattice”, Log. J. IGPL 13, No. 5, 543–550 (2005; Zbl 1088.06005)]): We define generalized Chu spaces and show that they together with (a special type of) their morphisms form a category. Moreover we define corresponding modifications of the image/inverse image operator and show their commutativity properties with mapping defining generalized concept lattice as fuzzifications of Zhang’s ones.

06B23 Complete lattices, completions
06D72 Fuzzy lattices (soft algebras) and related topics
68T30 Knowledge representation
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