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On fuzzy ideals in BCC-algebras. (English) Zbl 1018.06016

The authors investigate the properties of fuzzy BCC-ideals in BCC-algebras and their images. They prove as a main theorem:
Prop. 3.17: Every ascending chain of BCC-ideals of a BCC-algebra \(X\) terminates at finite steps if and only if the set of values of any fuzzy BCC-ideal in \(X\) is a well-ordered subset of \([0,1]\).
They also construct an extension of a fuzzy BCC-ideal \(\mu\) of a given BCC-subalgebra \(S\) of \(X\) to a fuzzy BCC-ideal \(\overline \mu\) of \(X\) with the same image. This result, as they note, is obvious from Lemma 4.1 of D. S. Malik and J. N. Mordeson’s paper: “Extensions of fuzzy subrings and fuzzy ideals” [Fuzzy Sets Syst. 45, 245-251 (1992; Zbl 0763.13004)].

MSC:

06F35 BCK-algebras, BCI-algebras

Citations:

Zbl 0763.13004
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Full Text: DOI

References:

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