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(Fuzzy) Ideals of BN-Algebras.

Research paper by Grzegorz G Dymek, Andrzej A Walendziak

Indexed on: 01 Jul '15Published on: 01 Jul '15Published in: TheScientificWorldJournal



Abstract

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.