By two relations belonging to (ϵ) and quasi-coincidence (q) between fuzzy points and fuzzy sets, we define the concept of (α, β)-fuzzy subalgebras where α, β are any two of {ϵ, q, ϵ Vq, ϵ Λq} with α ≠ϵ Λq. We state and prove some theorems in (α, β)-fuzzy BF-algebras.