This paper is in the formal concept analysis framework, an algebraic hierarchisation met- hod of data based on the notion of extent / intent, i.e. of maximally shared attributes and ob- jects. Here we present a correspondence-based similarity measure between two formal concept lattices, defined on an expressive model using correspondences between objects and between attributes of the two lattices. A key point of our approach is that the correspondences may not be mappings and may associate each object (resp. attribute) of one lattice with several objects (resp. attributes) of another one.