ON HYPER EQ-ALGEBRAS

Abstract

In this paper, we applied the hyper structures theory to EQ-algebras and we introduced the notion of hyper EQ-algebra which is a generalization of EQ-algebra.  In the following, we define the notions of good and separated hyper EQ-algebras and state and prove some properties of (good, separated) hyper EQ-algebras.  Moreover, by define the concept of (pre)filter, we construct the quotient hyper EQ-algebra.  Finally, we investigate the relation between hyper EQ-algebras and hyper BCK-algebras and (weak) hyper residuated lattices.