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Group decision-making is one important research part of decision-making science. As an extensive decision-making form, its theories and methods are widely used in the management activity of politics, economy, culture, military and others. It gives attention to many benefits of every aspects, overcomes the lack of knowledge, experience, ability, information of individual decision-maker, and has the important guiding sense for management decision-making, financial decision-making, investment decision-making, military decision-making and so on.Group decision-making studies aggregating methods from individual preferences to group preference, by which all alternatives of group decision-making problem could be ordered.In the chapter one, the research history and significance of group decision-making are introduced. We review the studies on the theories and methods of group decision-making and generalize the research background and the structure of this thesis. In the chapter two, the definitions and theories of bias mapping of group decision-making are introduced, and then the a-deviation number comparison rule of group decision-making is set up and it is proved that the rule satisfies some necessary conditions,with the help of a-deviation number comparison rule, a new sort method:a-deviation number method is set up. At the same time, we give a application case. In the chapter three, theκ-deviation number comparison rule of group decision-making is set up and it is proved that the rule satisfies some necessary conditions,with the help of k-deviation number comparison rule, a new sort method: k-deviation number method is set up. At the same time, we give a application case.In the chapter four, theακ-deviation number comparison rule of group decision-making is set up and it is proved that the rule satisfies some necessary conditions.,with the help ofακ-deviation number comparison rule, a new sort method:ακ-deviation number method is set up. At the same time, we give a application case. In the chapter five, the preference-ratio mapping and preference-ration axiom of group decision-making are introduced. We define the a-preference-ration mapping of group decision-making and that the a-preference-ration mapping satisfies some necessary conditions is proved.with the help of a-preference-ration mapping, a new sort method:a-preference-ration method is set up. An application case is gave in the end.
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