Linear operators strongly preserving natrices whose sign patterns require the perron property

We say that a sign-pattern matrix of B requires the Perron property if every real matrix A in Q(B) satisfies the Perron property. We characterize the linear operators that strongly preserve matrices whose sign patterns require the Perron property. We show that any such linear operator T is nonsingular and can be written as the direct sum of two linear operators, the first acting on diagonal matrices and the second acting on matrices with diagonal entries all zero.