Abstract
A fuzzy idea L of a Lie algebra L factors it into a Lie algebra L, L , called a fuzzy-quotient Lie algebra. This fuzzy-algebra Lie algebra is always a fuzzy partition of L and a fuzzy partition of L will be a fuzzy-quotient Lie algebra if and only if its associated fuzzy similarity relation is compatible with the Lie algebra operations. Relationship between the operations of the Lie algebras, L, I, T and Zadeh's extension principle are studied. We also study homomorphisms of Lie algebras and the relationship between them and fuzzy ideals and fuzzy subalgebras of the domains and the co-domains of these homomorphisms. Finally, solvability of fuzzy ideals and studied. In defining these solvable fuzzy ideals, we use Zadeh's extension principle.
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