ABSTRACT. In this paper we introduce the notion of BF -algebras, which is a generalization of B-algebras. We also introduce the notions of an ideal and a normal ideal in BF -algebras. We investigate the properties and characterizations of them.

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ABSTRACT. Characterizations of fuzzy filters in a BE-algebra are established. Conditions for a fuzzy set to be a fuzzy filter are given. For a fuzzy set µ the least fuzzy filter containing µ is constructed. The homomorphic properties of fuzzy filters of a BE-algebra are provided. Finally, characterizations of Noetherian BE-algebras and Artinian BE-algebras via fuzzy filters are obtained.