Hyper BZ-algebras and semihypergroups

Document Type : Original Article


School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi'an, China


In this paper, we introduce the new concept of a hyper BZ-algebra which is a generalization of BZ-algebra and hyper BCI-algebra, and give some examples and basic properties. We discuss the relationships among hyper BZ-algebras, hyper BCC-algebras and hyper BCI-algebra. Moreover, we propose the concepts of anti-grouped hyper BZ-algebras and generalized anti-grouped hyper BZ-algebras, and prove that the following important results:
(1) Every anti-grouped hyper BZ-algebra is an anti-grouped BZ-algebra;
(2) Every generalized anti-grouped hyper BZ-algebra corresponds to a semihypergroup.
Finally, we present a method to construct a new hyper BZ-algebra by using a hyper BCC-algebra and a standard generalized anti-grouped hyper BZ-algebra.