Study On Consensus Problems Of Group Decision Making

Group decision making (GDM) is widely used in real life as the main form of solving important and complicated decision problems. The main purpose of GDM is to find the consensus or a compromise. A key problem of multiple criteria group decision making (MCGDM) is to find the optimal solution on the condition of the maximum consistency and how to measure the consensus degree of the solution. Some problems on the consensus of GDM are investigated in this paper, with emphasis on consensus. First, the theories and methods of GDM and its consensus are generalized and summarized, the new definition and classification of GDM are proposed and three assumptions of the research of GDM are pointed out, and the model of the process of GDM is given. Second, the rules of GDM are studied in detail. As a result, two aggregation rules of the individual preference called "the rule of the maximum preference consensus" and "the rule of the maximum expected utility of the group" are presented. At the same time, in accordance with ties preference in the single rule, a compound rule of GDM is developed with which the ties problem can be solved successfully. And then, some common methods of GDM, such as the AHP method, the weighted geometric mean method (WGMM), the Borda-Kendall method, the minimum variance (MV) method, the clustering analytic method, the Cook-Seiford distance measure, Cb measure, the maximum and the minimum expected values, the concordance and discordance indices, etc., are used to discuss some consensus problems of GDM, including the consistency of the complex judgment matrix in AHP, the consensus methods of the aggregation of individual preferences; the aggregation of analytic hierarchy process methods based on similarities in decision makers' preferences, a consensus measure on multiple criteria group decision making. At last, the consensus problem in a GDM process is studied under incomplete information conditional on preference strength. This paper gives some new viewpoints, improves some methods of GDM, obtains some valuable conclusions, and establishes several applicable models. To some extent, the research in this paper makes a contribution to perfecting the theory and the methodology of GDM, and has great significance from the perspective of academic research and practical experience in this field.