  A complex fuzzy Lie algebra is a fuzzy Lie algebra whose membership function
takes values in the unit circle in the complex plane. In this paper, we deine
the complex fuzzy Lie subalgebras and complex fuzzy ideals of Lie algebras.
Then, we investigate some of characteristics of complex fuzzy Lie subalgebras.
The relationship between complex fuzzy Lie subalgebras and fuzzy Lie
subalgebras is also investigated. Finally, we define the image and the inverse
image of complex fuzzy Lie subalgebra under Lie algebra homomorphism. The
properties of complex fuzzy Lie subalgebras and complex fuzzy ideals under
homomorphisms of Lie algebras are studied.
