The authors consider fuzzy maximal ideals of BCI, BCK, and MV algebras, and show that such fuzzy ideals take only the values {0, 1}, and have level ideals which are maximal ideals of the algebra. It is shown that fuzzy maximal ideals of commutative BCK algebras are fuzzy prime. The authors establish a correspondence between ideals and fuzzy ideals. In a bounded BCK algebra, this correspondence is one-to-one between maximal ideals and fuzzy maximal ideals. The authors also show how to construct fuzzy ideals which are not characteristic functions of ideals of an MV algebra.
Fuzzy maximal ideals of BCI and MV-algebras / C. S., Hoo; Sessa, Salvatore. - In: INFORMATION SCIENCES. - ISSN 0020-0255. - STAMPA. - 80:3-4(1994), pp. 299-309. [10.16/0020-0255(94)90081-7]
Fuzzy maximal ideals of BCI and MV-algebras
SESSA, SALVATORE
1994
Abstract
The authors consider fuzzy maximal ideals of BCI, BCK, and MV algebras, and show that such fuzzy ideals take only the values {0, 1}, and have level ideals which are maximal ideals of the algebra. It is shown that fuzzy maximal ideals of commutative BCK algebras are fuzzy prime. The authors establish a correspondence between ideals and fuzzy ideals. In a bounded BCK algebra, this correspondence is one-to-one between maximal ideals and fuzzy maximal ideals. The authors also show how to construct fuzzy ideals which are not characteristic functions of ideals of an MV algebra.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
