(Fuzzy) Ideals of BN-Algebras

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...

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Bibliographic Details
Published in:TheScientificWorld 2015, Vol.2015 (2015), p.1-9
Main Authors: Dymek, Grzegorz, Walendziak, Andrzej
Format: Article
Language:English
Subjects:
Algebra
Fuzzy algorithms
Fuzzy logic
Fuzzy sets
Fuzzy systems
Mathematical research
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Summary: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 fuzzyset 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.
ISSN:2356-6140
1537-744X
1537-744X
DOI:10.1155/2015/925040