Lie algebras are so-named in honor of Sophus Lie, a Norwegian mathematician who pioneered the study of these mathematical objects. Lie's discovery was tied to his investigation of continuous transformation groups and symmetries. The structure of the laws in physics is largely based on symmetries. The objects in Lie theory are fundamental, interesting and innovat-ing in both mathematics and physics. It has many applications to the spectroscopy of molecules, atoms, nuclei and hadrons.
　　Our aim in this paper is to introduce and study a new sort of fuzzy Lie subalgebra (ideal) of a Lie al-gebra called -fuzzy Lie subalgebra (ideal). These fuzzy Lie subalgebras (ideals) are character-ized by their level ideals. Finally, we give a generali-zation of -fuzzy Lie subalgebras (ideals).