Generalization of One-Sided Concept Lattices

Abstract

We provide a generalization of one-sided (crisp-fuzzy) concept lattices, based on Galois connections. Our approach allows analysis of object-attribute models with different structures for truth values of attributes. Moreover, we prove that this method of creating one-sided concept lattices is the most general one, i.e., with respect to the set of admissible formal contexts, it produces all Galois connections between power sets and the products of complete lattices. Some possible applications of this approach are also included.