Denniston, Jeffrey T.; Melton, Austin; Rodabaugh, Stephen E. Formal concept analysis and lattice-valued Chu systems. (English) Zbl 1320.06004 Fuzzy Sets Syst. 216, 52-90 (2013). 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. Reviewer: Jiří Močkoř (Ostrava) Cited in 1 ReviewCited in 6 Documents MSC: 06A15 Galois correspondences, closure operators (in relation to ordered sets) 06B75 Generalizations of lattices 68T30 Knowledge representation Keywords:formal contexts; formal \(L\)-contexts; Galois connections; Chu systems; topological systems; formal context interchange PDFBibTeX XMLCite \textit{J. T. Denniston} et al., Fuzzy Sets Syst. 216, 52--90 (2013; Zbl 1320.06004) Full Text: DOI