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Fuzzy Soft Lie Algebras
Muhammad Akram, Bijan Davvaz and Feng Feng

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 (∈,∈ ∨q)− fuzzy soft Lie subalgebra which is a generalization of a fuzzy soft Lie subalgebra. We also introduce (∈α, ∈α ∨qβ)-fuzzy soft Lie subalgebras and describe some of their properties.

Keywords: ∈-soft set and a q-soft set, fuzzy soft Lie subalgebras; (∈,∈ ∨q)-fuzzy soft Lie subalgebras, (∈α, ∈α ∨qβ)-fuzzy Lie subalgebras

2000 Mathematics Subject Classification: 17B99, 03E72, 20N25

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