On Fuzzification of n-Lie Algebras

Abstract

The aim of this paper is to introduce the notion of intuitionistic fuzzy Lie subalgebras and intutionistic fuzzy Lie ideals of n-Lie algebras. It is a generalization of intuitionistic fuzzy Lie algebras. Then, we investigate some of characteristics of intutionistic fuzzy Lie ideals (resp. subalgebras) of n-Lie algeras. Finally, we define the image and the inverse image of intuitionistic fuzzy Lie subalgebra under
n-Lie algebra homomorphism. The properties of intuitionistic fuzzy n-Lie subalgebras and intuitionistic fuzzy Lie ideals under homomorphisms of n-Lie algebrasare studied. Finally, we define the intuitionistic fuzzy quotient n-Lie algebra by an intuitionistic fuzzy ideal of n-Lie algebra and prove that it is a n-Lie algebra.

Key words and phrases. n-Lie algebras; n-Lie homomorphism, intutionistic fuzzy set, intuitionistic fuzzy n-Lie subalgebra, intuitionistic fuzzy n-Lie ideal.

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