On Fuzzification of n-Lie Algebras

TL;DR

This paper extends the concept of fuzzy Lie algebras to n-Lie algebras, introducing intuitionistic fuzzy Lie subalgebras and ideals, and explores their properties, images, and quotient structures under homomorphisms.

Contribution

It introduces the notion of intuitionistic fuzzy Lie subalgebras and ideals for n-Lie algebras, expanding fuzzy algebra concepts to higher-order structures.

Findings

Defined intuitionistic fuzzy Lie subalgebras and ideals for n-Lie algebras.

Studied properties of these fuzzy structures under homomorphisms.

Established the formation of quotient n-Lie algebras with fuzzy ideals.

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 algebras are 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.