Anti complex fuzzy Lie subalgebras under S-norms

The objectives of this article are to present the notions of anti complex fuzzy subalgebras and anti complex fuzzy ideals of Lie algebras under  S-norms and we prove that the level subset of them are also subalgebras and ideals of Lie algebras, respectively. Next, we introduce the union and summation of them and we prove that the union and summation of them are also anti complex fuzzy subalgebras and anti complex fuzzy ideals of Lie algebras under  S-norms, respectively.  Finally, we investigate the homomorphic image (pre-image)  of them under Lie homomorphisms.