Hyper BL-algebras

Abstract

We put forth the concept of hyper BL-algebras which is a generalization of BL-algebras. We give some non-trivial examples and properties of hyper BL-algebras. Moreover, we introduce weak filters and weak deductive systems of hyper BL-algebras and study the relationships between them. Then we state and prove some theorems about weak filters and weak deductive systems. In particular, we define the concept of regular compatible congruence on hyper BL-algebras and construct the quotient structure in hyper BL-algebras. Finally, we discuss the conditions in which a quotient hyper BL-algebra is an MV-algebra.