Djouadi, Yassine; Prade, Henri Interval-valued fuzzy Galois connections: algebraic requirements and concept lattice construction. (English) Zbl 1205.68403 Fundam. Inform. 99, No. 2, 169-186 (2010). Summary: Fuzzy formal concept analysis is concerned with formal contexts expressing scalar-valued fuzzy relationships between objects and their properties. Existing fuzzy approaches assume that the relationship between a given object and a given property is a matter of degree in a scale \(L\) (generally [0,1]). However, the extent to which “object \(o\) has property \(a\)” may be sometimes hard to assess precisely. Then it is convenient to use a sub-interval from the scale \(L\) rather than a precise value. Such formal contexts naturally lead to interval-valued fuzzy formal concepts. The aim of the paper is twofold. We provide a sound minimal set of algebraic requirements for interval-valued implications in order to fulfill the fuzzy closure properties of the resulting Galois connection. Secondly, a new approach based on a generalization of Gödel implication is proposed for building the complete lattice of all interval-valued fuzzy formal concepts. Cited in 13 Documents MSC: 68T30 Knowledge representation 03B52 Fuzzy logic; logic of vagueness 06A15 Galois correspondences, closure operators (in relation to ordered sets) 06B75 Generalizations of lattices 68T37 Reasoning under uncertainty in the context of artificial intelligence Keywords:formal concept analysis; Interval-valued fuzzy formal contexts; Algebraic closure operators; Extended Gödel implication; Concepts lattice construction PDFBibTeX XMLCite \textit{Y. Djouadi} and \textit{H. Prade}, Fundam. Inform. 99, No. 2, 169--186 (2010; Zbl 1205.68403) Full Text: DOI