In this paper, we define the conceps of complex fuzzy Lie subalgebras and complex
fuzzy ideals of Lie algebras with respect to t-norms and investigate some of characteristics and
relationship between them. Next, we introduce the concepos of quotient subalgebras, intersection, sum and direct product of them and prove some results about them. Finally, we introduce
and study the image and the inverse image of them under Lie algebra homomorphisms.