Scalarization, Optimality Conditions and Group Decision Making

Abstract

Scalarization means the replacement of multiobjective optimization problem by a scalar objective optimization problem. First, we will present the conditions of the existence of such scalar objective with general binary relation and vector ordering uhich generalize Jahn’s results ([1]). Secona, ue uill utilize this scalar objective to present two ideas of group decision making uhich generalize Tanino-Nakayama-Sauaragi’s results ([2]). Third, for Lipshitz continuous multiobjective problem with general domination structure, ue uill present the necessary ana sufficient conditions of weak efficient solution(nondominated solution) ([3]), meanuhile, as a consequence, a necessary and sufficient conditions of group weak efficient point is obtained.