Concept lattices associated with interval-valued L-fuzzy contexts

In 1882 Wille published the paper titled Restructuring lattice theory: an approach based on hierarchies of concepts, where he developed a new theory called formal concept theory. In that paper he analyzes 0/1 relations between the object and attribute sets. Applying the L-fuzzy set theory to Wille’s results, we have developed the L-fuzzy concept theory dealing with L-fuzzy relations inside 0/1 relations. The final purpose of our theory is knowledge acquisition and classification. Taking as departure point the L-fuzzy concept theory, in this paper we study contexts defined by interval-valued L-fuzzy relations between the object and attribute sets. We give a new definition of L-fuzzy concept valid for this case and analyze the structure of the L-fuzzy concept set. We apply these results to a medical example.