  The aim of this paper is to introduce the notion of intuitionistic fuzzy Lie
subalgebras and intutionistic fuzzy Lie ideals of n-Lie algebras. It is a
generalization of intuitionistic fuzzy Lie algebras. Then, we investigate some
of characteristics of intutionistic fuzzy Lie ideals (resp. subalgebras) of
n-Lie algeras. Finally, we define the image and the inverse image of
intuitionistic fuzzy Lie subalgebra under n-Lie algebra homomorphism. The
properties of intuitionistic fuzzy n-Lie subalgebras and intuitionistic fuzzy
Lie ideals under homomorphisms of n-Lie algebras are studied. Finally, we
define the intuitionistic fuzzy quotient n-Lie algebra by an intuitionistic
fuzzy ideal of n-Lie algebra and prove that it is a n-Lie algebra.
