Some types of generalized fuzzy filters of BLBL-algebras

The aim of this paper is to introduce the notions of interval valued (∈,∈∨q)(∈,∈∨q)-fuzzy Boolean (implicative, positive implicative and fantastic) filters in BLBL-algebras and to investigate some related properties. Some characterizations of these generalized fuzzy filters are derived. Finally, the relations among these generalized fuzzy filters are discussed. It is proved that an interval valued (∈,∈∨q)(∈,∈∨q)-fuzzy filter in BLBL-algebras is an interval valued (∈,∈∨q)(∈,∈∨q)-fuzzy Boolean (implicative) filter if and only if it is both an interval valued (∈,∈∨q)(∈,∈∨q)-fuzzy positive implicative filter and an interval valued (∈,∈∨q)(∈,∈∨q)-fuzzy fantastic filter.