Under appropriate assumptions three completeness theorems are proved. The first theorem shows that using only information on relative importance of criteria it is possible to construct as close as desired approximation for the unknown preference relation of a decision maker. According to the second theorem in order to find an unknown set of nondominated points for a finite set of feasible solutions it is sufficient to get some information on relative importance of criteria. The third theorem deals with a convergence to the unknown set of nondominated points.