Some results of fuzzy BCK-filters

Let X be a bounded BCK-algebra and f a fuzzy set in X. If a fuzzy BCK-filter μ in X satisfies that (i) f⩽ μ, (ii) for any fuzzy BCK-filter ν in X, f⩽ ν implies μ⩽ ν, then μ is said to be generated by f and denote μ by [ f) for short. In the present paper, we give a procedure to construct the [ f) by...

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Bibliographic Details
Published in:Information sciences 2000-12, Vol.130 (1), p.185-194
Main Author: Meng, Biao-Long
Format: Article
Language:English
Subjects:
(fuzzy) BCK-filter
BCK-algebra
Distributive lattice
Fuzzy BCK-filter generated by a fuzzy set
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Summary:Let X be a bounded BCK-algebra and f a fuzzy set in X. If a fuzzy BCK-filter μ in X satisfies that (i) f⩽ μ, (ii) for any fuzzy BCK-filter ν in X, f⩽ ν implies μ⩽ ν, then μ is said to be generated by f and denote μ by [ f) for short. In the present paper, we give a procedure to construct the [ f) by f. As applications of this result we prove that the set of all fuzzy BCK-filters in a bounded BCK-algebra forms a complete and infinitely distributive lattice.
ISSN:0020-0255
1872-6291
DOI:10.1016/S0020-0255(00)00075-X