Let $H_8$ be the unique noncommutative and noncocommutative eight dimensional semi-simple Hopf algebra. We first construct a weak Hopf algebra $\widetilde{H_8}$ based on $H_8$, then we investigate the structure of the representation ring of $\widetilde{H_8}$. Finally, we prove that the automorphism group of $r\left(\widetilde{H_8}\right)$ is just isomorphic to $D_6$, where $D_6$ is the dihedral group with order 12.