On hyper BI-algebras

In this paper, we introduce the notion of hyper BI-algebra and investigate some properties of it. Also, we state and prove some theorems which determine the rela-tionship among R/C/D/T and V-hyper BI-algebras un-der some conditions. Then we study the relation among hyper BI-algebra with some of other hyper logical alge-bras such as hyper BCI/BCK/K/B/BCC-algebras and show that under which condition these hyper structures coincide. In addition, we define hyper subalgebra and (weak) ideal of a hyper BI-algebra and obtain some re-sults and the relation between them. Finally, we con-struct the quotient structure of hyper BI-algebra and ex-amine the isomorphism theorems.