Concept lattices are indeed lattices. In this paper, we present a new relationship between lattices and graphs: given a binary relation I, we define an underlying graph DI , and find out the constitution in the set of cover elements of the minimum element of the concept lattice of I using the properties of DI . The following is to provide a way to establish a one-to-one correspondence between the set of covers of an element in the concept lattice and the set of covers of the minimum in a sublattice of the concept lattice. We apply the one-to-one correspondence to define a new underlying graph, and generate the elements of the lattice.
Digital Object Identifier (DOI)
"A Graph-Theoretic Method to Representing a Concept Lattice,"
Applied Mathematics & Information Sciences: Vol. 08
, Article 13.
Available at: https://dc.naturalspublishing.com/amis/vol08/iss2/13