Fuzzy Soft Lie Algebras

Fuzzy sets and soft sets are two different methods for representing vagueness and uncertainty. In this paper we apply these methods in combination to study vagueness and uncertainty in Lie algebras. We introduce the concept of fuzzy soft Lie subalgebras and investigate some of their properties. We discuss fuzzy soft image and fuzzy soft inverse image of fuzzy soft Lie subalgebras. We introduce the notion of an (is an element of, is an element of vq)-fuzzy soft Lie subalgebra which is a generalization of a fuzzy soft Lie subalgebra. We also introduce (is an element of(alpha), is an element of(alpha) Vq beta)-fuzzy soft Lie subalgebras and describe some of their properties.