Discussions on filters in BL-algebras

In this paper, we define σ-normal filters, σ-fantastic filters, σ-obstinate filters, σ-integralfilters, σ-semi-integral filters in BL-algebras, then we state and prove some theorems to characterize theseconcepts. In this paper, we begin an algebraic investigation of new types of σ-filters in BL-algebras; whichcontains definitions, and their relationship. Finally, equivalent conditions are provided for easier study ofthese types of filters in BL-algebras and some important classes of BL-algebras and their connections arepresented.