Automorphisms of normal partial transformation semigroups

We let X be an arbitrary infinite set. A semigroup S of total or partial transformations of X is called -normal if hSh -1 = S , for all h in , the symmetric group on X . For example, the full transformation semigroup , the semigroup of all partial transformations , the semigroup of all 1–1 partial transformations and all ideals of and are -normal.