On the use of irreducible elements for reducing multi-adjoint concept lattices

Looking for strategies to reduce the size of concept lattices is very important in formal concept analysis, when they preserve the main information of the relational database.This paper presents several properties of the useful fuzzy-attributes, in the general fuzzy case of multi-adjoint concept lattices and provides two mechanisms in order to reduce the size of concept lattices based on irreducible elements, without losing or modifying important information. Specifically, the reduced concept lattices are sublattices of the original one. Moreover, interesting properties of these mechanisms are studied and the relationship among both and other strategies is also introduced.