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 .