Fuzzy logic models in a category of fuzzy relations

Then SetF(Ω) is a category with Ω-sets as objects and maps f : A → B such that γ(f(x), f(y)) ≥ δ(x, y) for all x, y ∈ A as morphisms f : (A, δ) → (B, γ). Moreover, by SetR(Ω) we understand a category which is an analogy of a category of sets with relations between sets as morphisms. Objects of this category SetR(Ω) are the same as in the category SetF(Ω) and morphism f : (A, δ) → (B, γ) are maps f : A×B → Ω such that