×

Formal concept analysis and lattice-valued Chu systems. (English) Zbl 1320.06004

In this extended and well written paper the authors link many previous results in formal concept analysis (FCA) and its generalization to \(L\)-formal concept analysis (\(L\)-FCA), where \(L\) is an appropriate lattice structure, to Chu systems (and their generalization to \(L\)-Chu systems). Both systems are build from relationships between objects in one set and their attributes in another set. These relationships are based on Galois connection between \(L\)-Birkhoff operators. To show the relationships between these structures the authors use categorical framework for \(L\)-FCA and \(L\)-Chu systems represented by category \(L\)-\(\mathbf{FCI}\) of \(L\)-formal contexts in which morphisms preserve the \(L\)-Birkhoff operators and the category \(\mathbf{Chu}_L\) where morphisms are \(L\)-Chu transforms. Various functors between these categories and their subcategories are investigated.

MSC:

06A15 Galois correspondences, closure operators (in relation to ordered sets)
06B75 Generalizations of lattices
68T30 Knowledge representation
PDFBibTeX XMLCite
Full Text: DOI