Dick et al. introduced a relation $\leq ^*$ on $\Pi -i$ numbers and proved that $(\Pi -i, \leq ^*)$ is a bounded distributive complete lattice. In the present paper, we point out that the relation $\leq ^*$ is not a partial order and that $(\Pi -i, \leq ^*)$ is not a lattice. In addition, we study some partial orders on $\Pi -i$ numbers.