*Abigail Villa (Mindanao State University-Iligan Institute of Technology (MSU-IIT))
Let $H=\{0,1,2\}$ and consider the Cayley table
\[
\begin{array}{c|ccc}
\cas &0 &1 &2\\
\hline
\vspace{0.01em}
0&\{0\}&\{0\}&\{0\}\\
1&\{0,1,2\}&\{0,1\}&\{0,1\}\\
2&\{0,2\}&\{0,1,2\}&\{0,2\}
\end{array}
\]
By routine calculations, we see that $(H;\cas,0)$ satisfies all the properties of a hyper BCI-algebra except the requirement that $x \ll y$ and $y \ll x$ implies $x=y$. Notice in the table that if $x=0$ and $y=1$, we have $0\ll1$ and $1 \ll 0$ but $0\neq 1$. But a closer inspection suggests that this hyperalgebra satisfies the property $((x \cas y)\cas z)\ll (y \cas z),~\forall x,y,z\in H$. This leads to the conceptualization of hyper GR-algebras which is an ongoing study done by G. Petalcorin and R. Indangan. \\
\vspace{0.5em}
Let $H$ be a nonempty set and $\cas$ be a hyperoperation on $H$. Then $(H; \cas,0)$ is called a $hyper~GR-algebra$, if it contains a constant $0\in H$ and satisfies the following conditions, for all $x,y,z\in H$:\\
$(HGR_1):~((x\cas z)\cas (y\cas z)) \ll (x\cas y);$\\
$(HGR_2):~(x\cas y)\cas z = (x\cas z) \cas y;$\\
$(HRG_3):~x \ll x;$\\
$(HGR_4):~(0\cas (0 \cas x)) \ll x, x \neq 0$; and\\
$(HGR_5):~((x \cas y))\cas z \ll (y \cas z)$.\\
\vspace{0.5em}
This paper will deal on hyper homomorphism and some of its properties on hyper GR-algebra.