Another View of Fuzzy Filters of BL-Algebras

In this paper, we introduce some types of (is an element of, is an element of boolean OR q(k)(delta))-fuzzy filters of BL-algebras by applying the (delta,k)(delta,k)-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 (is an element of, is an element of boolean OR q(k)(delta))-fuzzy filters of BL-algebras. Further, we explore the relationships among (is an element of, is an element of boolean OR q(k)(delta))-fuzzy filters and other types of (is an element of, is an element of boolean OR q(k)(delta))-fuzzy filters and it is proved that every (is an element of, is an element of boolean OR q(k)(delta))-fuzzy Boolean (implicative) filter is a (is an element of, is an element of boolean OR q(k)(delta))-fuzzy positive implicative filter and (is an element of, is an element of boolean OR q(k)(delta))-fuzzy fantastic filter, but the converse may not be true. Furthermore, we establish the conditions under which an (is an element of, is an element of boolean OR q(k)(delta))-fuzzy positive implicative filter is an (is an element of, is an element of boolean OR q(k)(delta))-fuzzy Boolean (implicative) filter.