Similarity relations in concept lattices

This paper studies the issue of similarity relations in fuzzy concept lattices. Fuzzy concepts and fuzzy concept lattices represent a formal approach to the modelling of non-sharp (fuzzy) concepts and conceptual structures in the sense of traditional (Port-Royal) logic. Applications of concept lattices are in representation of conceptual knowledge and in conceptual analysis of (fuzzy) data. Similarity relations are defined and considered on three levels: similarity of objects (and similarity of attributes), similarity of concepts, and similarity of concept lattices. We show a way to factorize (simplify) concept lattices by the similarity of concepts. Also shown is how to reduce the computation of the similarity relations.