Attribute reduction in multi-adjoint concept lattices

Knowledge reduction is one of the key issues in formal concept analysis and there have been many studies on this topic. The irreducible elements in a lattice are also very important, since they form the basic information of a relational system. Moreover, they are also important from the viewpoint of attribute reduction.Both topics are notably more complicated in a fuzzy setting since not only the size of the sets of attributes and objects influence the size of the fuzzy concept lattice, but the truth-value sets, where the sets of objects, attributes and the relation are evaluated, are important.This paper presents, in the general fuzzy framework of multi-adjoint concept lattices, a characterization of the meet-irreducible elements, from which a classification of attributes and its application to attribute reduction is introduced.