Some Results on Fuzzy Basis of Fuzzy Lie Algebras

Abstract

This work explores the application of fuzzy set theory to the study of algebraic structures, with a particular focus on Lie algebras. Since fuzzy Lie algebra can be regarded as fuzzy vector space, the foundational properties of these structures are investigated, with emphasis placed on the role of fuzzy basis. A selection of key results is presented, establishing necessary and sufficient conditions for a basis to be fuzzy, and providing concrete examples to illustrate how these findings can be applied in practice to fuzzy Lie subalgebras.