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Zbl 0991.06015
Meng, Biaolong
Some results of fuzzy BCK-filters. (English)
[J] Inf. Sci. 130, No.1-4, 185-194 (2000). ISSN 0020-0255

Let $X$ be a bounded BCK-algebra and $f$ a fuzzy set in $X$. If a fuzzy BCK-filter $\mu$ (for the definition of BCK-filters, see {\it J. Meng}, Math. Jap. 44, 119-129 (1996; Zbl 0880.06012)) in $X$ satisfies (i) $f\le\mu$, (ii) for any fuzzy BCK-filter $\nu$ in $X$, $f\le\nu$ implies $\mu\le\nu$, then $\mu$ is said to be generated by $f$, and denote $\mu$ by $[f)$ for short. In this paper, the author gives a procedure to construct $[f)$ by $f$. As one application of this result the author proves that the set of all fuzzy BCK-filters in a bounded BCK-algebra forms a complete and infinitely distributive lattice.
[Jie Meng (Xian)]

MSC 2000:: *06F35 BCK-algebras, etc.

Keywords: bounded BCK-algebra; fuzzy BCK-filter

Citations: Zbl 0880.06012

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