The Research Of Some Issues In Groupdecision Making

Group decision making plays an important part in the field of decision making. It studies how to integrate individual preferences into group preference on a set of alternatives, so that the group can order all the alternatives or choose the optimal one. Thanks to the incomparable superiorities of group decision making compared with individual decision making, group decision making has become the burgeoning science which draws so many people's attention, and the research of group decision making has been a focus and significant frontier of the decision making research. Meanwhile, since the theories and methods of group decision making involve multitudinous subjects such as mathematics, management, economics, sociology, psychology and so on and its internal complication, the group decision making is still a weak section of the decision making theory, and many problems in group decision making need to be futher researched. Some uncertain problems in group decision making were studied as follwing:In chapter one, the related theories of group decision making and the background and significance of its research are introduced, and the research history of group decision making is reviewed. Finally, the research status of the various branches of the group decision making problems studied in this paper are analysed and arranged systematically.In chapter two, a cardinal incomplete information mapping based on individual mark from individual to group is proposed for incomplete information group decision making problems,. and the properties of this mapping and the rational conditions the mapping satisfies are discussed ; then a method for cardinal incomplete information group decision making is constructed.In chapter three, the incomplete information Borda number mapping is proposed for the group decision making problems of incomplete information, , and the properties and the relationship with the Arrow preference axioms of the mapping are discussed; then, the Borda number rule under the condition of incomplete information is constructed, which in an expansion of the Borda number rule for the pure preference pattern.In chapter four, the group decision making problems under the condition that the individuals and group both have stochastic preference structure are studied for group decision making with stochastic preference, and the concept of group stochastic preference mapping from individual stochastic preferences to group stochastic preference is introduced. Then a set of preference axioms is given and the corresponding impossibility theorem is proved.In chapter five, the rational conditions and the relationship with the Arrow preference axioms of the existing compound group sequencing method are studied. Then a cardinal compound group sequencing method based on individual mark is proposed and the various properties of this method and the rational conditions satisfied by this method are discussed.