Abstract
The authors introduce the notions of (\(\in, \in \vee q\))-fuzzy Boolean (implicative, positive implicative, and fantastic) filters in BL-algebras, present some characterizations on these generalized fuzzy filters, and describe the relations among these generalized fuzzy filters. It is proved that an (\(\in, \in \vee q\))-fuzzy filter in a BL-algebra is Boolean (implicative) if and only if it is both positive implicative and fantastic.
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