Interval valued (∈, ∈ V q)-fuzzy filters of pseudo BL-algebras

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued (is an element of, is an element of V q)-fuzzy filters of pseudo BL-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these generalized interval valued fuzzy filters of pseudo BL-algebras is considered. Finally, we consider the concept of implicationbased interval valued fuzzy implicative filters of pseudo BL-algebras, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.