∨ ) ∈ ∈ , - fuzzy Lie subalgebra and ideals

generalization of Rosenfeld's fuzzy subgroup, and Bhakat and Das's fuzzy subgroup is given in [20]. 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 innovating in both mathematics and physics. It has many applications to the spectroscopy of molecules, atoms, nuclei and hadrons. Algebraic structures play a prominent role in mathematics with wide ranging applications in many disciplines such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, topological spaces and the like. This provides sufficient motivation to researchers to review various concepts and results from the realm of abstract algebra in the broader framework of fuzzy setting. Our aim in this paper is to introduce and study a new sort of fuzzy Lie subalgebra (ideal) of a Lie algebra called ( ) q ∨ ∈ ∈, -fuzzy Lie subalgebra (ideal). These fuzzy Lie subalgebras (ideals) are characterized by their level ideals. Finally, we give a generalization of ( ) q ∨ ∈ ∈, -fuzzy Lie subalgebras (ideals). Our aim in this paper is to introduce and study a new sort of fuzzy Lie subalgebra (ideal) of a Lie algebra called -fuzzy Lie subalgebra (ideal). These fuzzy Lie subalgebras (ideals) are characterized by their level ideals. Finally, we give a generalization of -fuzzy Lie subalgebras (ideals). ( q ∨ ∈ ∈, )