On the rank of the certain orthodox semigroups

Let $X_{n}=\{1, 2, \ldots, n\}(n\geq 4)$ be natural order set,$W_{n}$ be semigroup of the order-preserving and compressing singular transformations on $X_{n}$,$RW_{n}$ be regular subsemigroup consisting of all regular elements in $W_{n}$.By Green equivalence and eggbox graph,we obtained that rank of ideals $I_{r} =\{\alpha\in RW_{n}:\mid$im$\alpha\mid\leq r\}(1\leq r\leq n-1)$ be $n-r+1$ .