It is known that the ranks of the semigroups $mathcal{SOP}_n$, $mathcal{SPOP}_n$ and $mathcal{SSPOP}_n$ (the semigroups of orientation preserving singular self-maps, partial and strictly partial transformations on $X_n={1,2,{ldots},n}$, respectively) are n, 2n and n + 1, respectively. The idempotent rank, defined as the smallest number of idempotent generating set, of $mathcal{SOP}_n$ and $mathcal{SSPOP}_n$ are the same value as the rank, respectively. Idempotent can be seen as a special case (with m = 1) of m-potent. In this paper, we investigate the m-potent ranks, defined as the smallest number of m-potent generating set, of the semigroups $mathcal{SOP}_n$, $mathcal{SPOP}_n$ and $mathcal{SSPOP}_n$. Firstly, we characterize the structure of the minimal generating sets of $mathcal{SOP}_n$. As applications, we obtain that the number of distinct minimal generating sets is $(n-1)^nn!$. Secondly, we show that, for $1{leq}m{leq}n-1$, the m-potent ranks of the semigroups $mathcal{SOP}_n$ and $mathcal{SPOP}_n$ are also n and 2n, respectively. Finally, we find that the 2-potent rank of $mathcal{SSPOP}_n$ is n + 1.