Applied Mathematics & Information Sciences

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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.

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