This study is based on the structure of pseudo hyper GR-algebra, an algebra that is partially related on some class of hyper BCI-algebras. This allows us to create a new structure and how this two algebras are related to each other. A pseudo hyper GR-algebra involves two hyper operations and a set of axioms that come in pairs or a combination of both making it interesting like some algebras established. This paper focuses on some properties of pseudo hyper GR-algebras and its ideals. Moreover, pseudo hyper GR-ideals were dened and classied to determine their relationship to each other.

European Journal of Pure and Applied Mathematics Vol. 12, No. 3