Lie algebras were proposed by
Sophus Lie and there are many applications of them in several branches of
physics. The notion of fuzzy sets was introduced by Zadeh and manymathematicians have been involved in extending the concepts and results ofabstract Lie algebra to fuzzy theory.
This paper is the continuation of the
results obtained in, where we presented conditions to generalize the concepts
of solvable and nilpotent radicals of Lie algebras (called of solvable and
nilpotent fuzzy radicals, respectively) to a class of fuzzy Lie algebras. Inthis article we use the solvable fuzzy radical to generalize the structuretheorem of semisimple Lie algebras and the Levi’s decomposition theorem to aclass of the fuzzy Lie algebras. The results presented in this paper are still
strongly connected with results proved in.
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