Another view of fuzzy filters of BL-Algebras

In this paper, we introduce some types of [Formula: see text]-fuzzy filters of BL-algebras by applying the [Formula: see text]-quasi-coincident relation. By using a level subset of a fuzzy set in a BL-algebra, we study some characterizations of these generalized fuzzy filters and investigate several properties of [Formula: see text]-fuzzy filters of BL-algebras. Further, we explore the relationships among [Formula: see text]-fuzzy filters and other types of [Formula: see text]-fuzzy filters and it is proved that every [Formula: see text]-fuzzy Boolean (implicative) filter is a [Formula: see text]-fuzzy positive implicative filter and [Formula: see text]-fuzzy fantastic filter, but the converse may not be true. Furthermore, we establish the conditions under which an [Formula: see text]-fuzzy positive implicative filter is an [Formula: see text]-fuzzy Boolean (implicative) filter.