The notion of Λ-fuzzy set was introduced by M. E. EI-Shafei and A. Zakari in 2006 [θ-Generalized closed sets in fuzzy topological spaces, The Arabian Journal for Science and Engineering, Vol. 31, Number 2A]. 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 Λ γ -sets that includes the class of all fuzzy γ-open sets. It also introduces the notion of fuzzy V γ -sets as the dual concept of fuzzy Λ

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... γ 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 Λ bcontinuity [Gulhan Aslim, Gizem Gunel On fuzzy Λ b -sets and fuzzy Λ b -continuity. Chaos, Solitons and Fractals 42 (2009). 1024-1030 called fuzzyΛ γ -continuity is introduced and the relationships are also established with the already existing functions accordingly. Finally, fuzzy Λ γ -Generalized closed sets are defined and studied with some of their applications.