The Research Of Synthetical Efficient Number Method For Group Multi--objective Decision Making

Group multiobjective decision making is a new cross research field between group making and multiobjective programming.Its theory and methods have a broad applications in modern societies and complicated decision making problem.This paper first briefly introduces the forming background and research status of multi-objective programming and group decision making; Then introduces the class of synthetical major joint efficient solutions in group multiobjective decision making,Its necessary and sufficient conditions are studied.Futher,the geometric charactertizations of synthetical major joint efficient solutions in group multiobjective decision making are proved;the concept of group synthetical efficient preference for group multiobjective decision making problem are defined.A synthetical efficient mapping from individual preferences to group preference is constructed.Based on some fundamental properties of mapping,a method of synthetical efficient ordering alternative for group multiobjective decision making in given;Finally,the strong-weak synthetical major efficient solutions of group multiobjective decision making in lexicographic order are studied,and get the related theory and properties of group multiobjective decision making.