The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are
investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are
displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given.
The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals
of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are
obtained