Abstract:

Group decision-making is to integrate group intelligence by assigning reasonable weights to experts. The distribution of expert weight not only can be determined subjectively by the reputation of experts， but also can be determined objectively by the quality of expert decision-making information， which is generally judged by the consistency test. The information with good consistency is effective information， otherwise is ineffective information. The effectiveness of group decision can only be guaranteed by integrating effective information. In the practice of group decision making， experts may have differences in their judgment of the importance of the same indicator， and all experts may have differences in different indicators. The information given by experts may be effective in some indicators and ineffective in other indicators. Therefore， the consistency test results based on different indicators will be different， which means considering a single indicator or all indicators may give different consistency results. The existing method of expert weight is distributed by decision experts’ consistency test result based on all indicators. The information of the experts on all indicators is considered as a whole. The expert information that fails the consistency test will be eliminated， or corrected until it passes the consistency test. The consistency test based on all indicators hides the difference of expert decision information on different indicators， so the effective information and ineffective information cannot be effectively distinguished. It may retain the ineffective information of the experts who have passed the consistency test， and delete the effective information of the experts who have not passed the consistency test， which obviously affects the rationality of the group decision results. This study is proposed to test the decision information consistency of the decision expert from the index level， effectively distinguish effective and ineffective information from the same expert’s decision information. Based on the G1 subjective weighting method， the expert weight distribution method under the expression of accurate value and interval value is studied. First， based on the G1 weighting method， a consistency test method based on the index level is proposed under the condition of accurate value. The criteria for effective and ineffective information in the weight information are determined， and an optimization model is established to solve the optimal combination weight. Then， the above framework is extended from the precise number to the interval number. The criteria for good and bad information under the interval number， the consistency test method， and the optimization problem of weight determination are proposed. Finally， the effectiveness and feasibility of the proposed group decision combination weighting method are verified by an actual example. Different from the existing research， the effective and ineffective decision-making information of the decision experts is effectively distinguished. The consistency test is carried out at the index level instead of at the expert level， which makes up for the shortcoming of traditional consistency test， such as loss effective information from ineffective experts and misuse ineffective information from effective experts.

Key words: group decision making, consistency test, interval number, G1