The notion of Λ-fuzzy set was introduced by M. E. EI-Shafei and A. Zakari in 2006 . We examine some basic properties of it and prove some characterization theorems for the same. The paper presents a new class of fuzzy sets called fuzzy Λγ-sets that includes the class of all fuzzy γ-open sets. It also introduces the notion of fuzzy Vγ-sets as the dual concept of fuzzy Λγ sets to study the spaces constituted by those sets and obtain a completely different structure which is called fuzzy independent Alexandorff space. A stronger form of fuzzy Λb - continuity called fuzzy Λγ-continuity is introduced and the relationships are also established with the already existing functions accordingly. Finally, fuzzy Λγ-Generalized closed sets are defined and studied with some of their applications.