Abstract: By two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets, the concept of (α,β)-fuzzy B-algebras, which is a generalization of fuzzy B-algebras, in a B-algebra is introduced where α,β are any two of ｛∈,q,∈∨q,∈∧q｝ with α≠∈∧q, and related properties are investigated. It is found that the most viable generalization of Jun’s fuzzy B-algebra obtained in this way, is the concept of (∈,∈∨q)-fuzzy B-algebra. How the homomorphic images and inverse images of (∈,∈∨q)-fuzzy B-algebra becomes (∈,∈∨q)-fuzzy B-algebra is studied.