(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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Veröffentlicht in:	TheScientificWorld 2015, Vol.2015 (2015), p.1-9
Hauptverfasser:	Dymek, Grzegorz, Walendziak, Andrzej
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Fuzzy algorithms Fuzzy logic Fuzzy sets Fuzzy systems Mathematical research
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Beschreibung
Zusammenfassung:	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