Relationship Between Hyper MV -algebras and Hyperlattices

Abstract

Abstract. Sh. Ghorbani, et al. [9], generalized the concept of M V -algebras and defined the notion of hyper M V -algebras. Now, in this paper, we try to prove that any hyper M V -algebra is a hyperlattice. First we prove that any hyper M V -algebra that satisfies the semi negation property is a hyperlattice. Then with a computer program, we show that any hyper M V -algebra of order less than 6, is a hyperlattice. Finally, we claim that this result is correct for any hyper M V -algebra.