FUZZY IDEALS AND FUZZY SUBALGEBRAS OF LIE-ALGEBRAS

A fuzzy ideal I of a Lie algebra L factors it into a Lie algebra L/I, called a fuzzy-quotient Lie algebra. This fuzzy-quotient Lie algebra i s 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 similar ity relation is compatible with the Lie algebra operations. Relationsh ip between the operations of the Lie algebras L/I, L and Zadeh's exten sion principle are studied. We also study homomorphisms of Lie algebra s and the relationship between them and fuzzy ideals and fuzzy subalge bras of the domains and the co-domains of these homomorphisms. Finally , solvability of fuzzy ideals are studied. In defining these solvable fuzzy ideals, we use Zadeh's extension principle.