Complex Fuzzy Lie Algebras

Abstract

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 define 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.

Key words and phrases. Lie algebras; Lie homomorphism; π-fuzzy set; π-fuzzy Lie subalgebra; homogeneous complex fuzzy set; complex fuzzy Lie subalgebra; complex fuzzy Lie ideal.

2000 Mathematics Subject Classification. 08A72, 03E72, 20N25