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.

An overview of hyper logical algebras

“…Specially, they An overview of hyper logical algebras 33 proved that any linearly ordered hyper MV-algebra is a strongly commutative symmetric hyper equality algebra and under some conditions, any strongly commutative involutive hyper equality algebra is a hyper MV-algebra. In [32], Xin defined the concept of hyper BL-algebras which is a generalization of BL-algebras. He gave some non-trivial examples and properties of hyper BLalgebras.…”

“…Let H = ⟨H; ∼, ∧, 1⟩ be a hyper equality algebra. We say that H has (I) or (II) properties, if, for any x, y ∈ H, H satisfies the following conditions: In [32], Xin put forth the concept of hyper BL-algebras which is a generalization of BL-algebras. He gave some non-trivial examples and properties of hyper BL-algebras.…”