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Fuzzy Boolean and positive implicative filters of BL-algebras. (English) Zbl 1072.03037
Summary: The aim of this paper is to introduce the notions of fuzzy Boolean filters and fuzzy positive implicative filters in BL-algebras and to investigate their properties. Several characterizations of fuzzy Boolean filters and fuzzy positive implicative filters are derived. Extension theorems of fuzzy Boolean filters and fuzzy positive implicative filters are obtained. The relation between fuzzy Boolean filters and fuzzy positive implicative filters is investigated and it is proved that every fuzzy Boolean filter is a fuzzy positive implicative filter, but the converse may not be true. Furthermore, conditions under which a fuzzy positive implicative filter is a fuzzy Boolean filter are established.
03G25Other algebras related to logic
03B52Fuzzy logic; logic of vagueness