  The concepts of $(\overline{\in},\overline{\in} \vee \overline{q})$-fuzzy
(implicative, positive implicative and fantastic) filters of $BL$-algebras are
introduced and some related properties are investigated. Some characterizations
of these generalized fuzzy filters are derived. In particular, we describe the
relationships among ordinary fuzzy (implicative, positive implicative and
fantastic) filters, $(\in,\ivq)$-fuzzy (implicative, positive implicative and
fantastic) filters and $(\overline{\in},\overline{\in} \vee
\overline{q})$-fuzzy (implicative, positive implicative and fantastic) filters
of $BL$-algebras. Finally, we prove that a fuzzy set $F$ on a $BL$-algebra $L$
is an $(\overline{\in},\overline{\in} \vee \overline{q})$-fuzzy implicative
filter of $L$ if and only if it is both $(\overline{\in},\overline{\in} \vee
\overline{q})$-fuzzy positive implicative filter and an
$(\overline{\in},\overline{\in} \vee \overline{q})$-fuzzy fantastic filter.
