On ($$\in, \in \vee q$$)-Fuzzy Filters of BL-Algebras

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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