  Relations among the effective hadron masses and the effective interactions in
nuclear matter are studied by using the generalized relativistic mean field
theory. We found that we can make the effective omega-meson mass smaller and
the equation of state softer if we require that the omega-meson mean field is
proportional to the baryon density. In this case, there is a simple and exact
relation between the effective omega-meson mass and the effective omega-nucleon
coupling. Because of this relation, the effective omega-nucleon coupling
automatically decreases if the effective omega-meson mass decreases.
Consequently, the equation of state becomes softer. A trial to embed the QCD
sum-rule results into the hadron field theory is also shown.
