The Research Of Some Theoriesand Methods In Groupdecision Making

Group decision making is an important branch of modern decision-making science, which is also known as collective choice or social choice in economic and political fields. Its main purpose is to analyze how to integrate individual preference into a group preference, and then two possible results can be got by the method. The first is the order of the alternatives, the second is help the qo choice the optimal one. Where the preference on something or the set of alternatives is made by every person on a set. What group decision making embody is a negotiation results of the participants, which is more reliable and fairness than individual decision or dictatorial. At the same time, group decision making is a cross-discipline, its theory and methods related to social choice, operational research, management science, economics, psychology and many other disciplines. And thus, group decision making problem have caused widespread concern of scholars in difference realms, especially about its research and application in decision supporting system and investment science. In this thesis, we illustrate and study some issues in group decision making, and arrange the details as follows:In the first chapter, we presentation the research background and significance of group decision making theory in domestic and international. And for the problem, we give a brief introduction about the basic concepts and theories. The following is the Arrow conditions of impossibility and the impossibility theorem. At last, some ranking rules are given which are widely used in our around.In the second chapter, we define a choice function, by means of it we could study the k-Preference Deviation Rule in Group Decision Making, we prove it satisfies four axioms which is first studied by Arrow, but k-Preference Deviation Rule does not satisfy transmission property, in order to give the ordering, we present the definition of choice function, it can resolve the ordering problem where the rule is not transfer .In the third chapter, we unify ordinal representation form and cardinal representation form by Blin-method which is studied in fuzzy mathematics. And verify the Blin-method satisfies four of the Arrow axioms and some other properties. And discussed the existence conditions of group optimal solutions, at the last we give the ranking method and example analysis.In the fourth chapter, a utility aggregation function is introduced and proved that the combination of four axioms which have been known is just a sufficient and necessary conditions of the function of utility aggregation. At last, we give the algorithms about order of the group.The last chapter, the threshold function problem which is under the cardinal form will be studied. We get the mutual relation of them and the corresponding rank about them.