States on hyper MV-algebras

Abstract

In this paper, we introduce and study states on hyper MV -algebras. First, we introduce the notions of Riey states and Bosbach states on a hyper MV -algebra and derive some properties of them. Also, we investigate and characterize regular Riey can states and regular Bosbach states on a hyper MV -algebra. Moreover, using a Bosbach state on a hyper MV -algebra, we construct and discuss a quotient hyper MV -algebra. In particular, we obtain some equivalent conditions under which a quotient hyper MV -algebra becomes a Boolean algebra. Finally, we introduce the notion of state morphisms on hyper MV -algebras, and discuss some relationships between state morphisms and Bosbach states.