Several authors generalized the conjugation in the sense of Fenchel so that it is not realized with respect to the (component-wise) continuous bilinear form (x, y) overX×Y(a – dual – topological pair), but that this is replaced by an arbitrary coupling functional ϕ ∈ RX×Y. Properties of such functionalsjhave been studied, which, by means of a twofold conjugation with respect to ϕ, are transformed into themselves. The aim of this paper is to give a set-theoretic description by means of the epigraph of these functionals, which proves to be equivalent to the analytical one.