The paper deals with the isomorphism between the constraint heterogeneous concept lattices and concept lattices with heterogeneous hedges. The essential point of the former approach encompasses the full diversification of data structures within a formal context. In particular, we use a different complete lattice for diverse objects, a different complete lattice for diverse attributes and a different poset for diverse matrix fields. The latter framework with heterogeneous hedges results in a reduction in the size of the corresponding concept lattice. We present the properties of constraint heterogeneous approach that is associated with the fixpoints of hedges and we add remarks to the related studies. (C) 2015 Elsevier B.V. All rights reserved.