Relating generalized concept lattices and concept lattices for non-commutative conjunctors

Generalized concept lattices have been recently proposed for dealing with uncertainty or incomplete information as a non-symmetric generalization of the theory of fuzzy formal concept analysis. On the other hand, concept lattices have been defined as well in the framework of fuzzy logics with non-commutative conjunctors.The contribution of this work is to prove that any concept lattice for non-commutative fuzzy logic can be interpreted inside the framework of generalized concept lattices; specifically, it is isomorphic to a sublattice of the cartesian product of two generalized concept lattices.