群决策中基于判断相似度的专家聚类及群体意见集结方法

摘要/Abstract

摘要： 针对大规模群决策问题,提出了一种基于专家意见相似度的群体判断信息逐步集结规划的方法。首先利用备选方案序关系向量的灰色关联度和夹角余弦构造两两专家判断信息的组合相似度;其次以判断相似度为标准,采用一种广度邻居搜索算法对专家进行聚类;然后以判断偏差最小为目标,构造非线性的约束规划模型对每一类专家意见进行集结,从而获得类内专家的集结信息;最后从专家数量最多的类别开始,依次对每类专家集结后的判断信息进行再次集结,从而获得最终的评判结果。该方法将大规模的复杂群决策转化为低复杂度的多阶段专家信息集结问题,并保证了群体结果的一致性。算例分析验证了方法的可行性和有效性。

关键词: 群决策, 判断信息, 组合相似度, 一致化, 集结

Abstract: This paper proposes an expert classification and group consensus method for group decision-making based on combined similarity degree which consists of gray correlation degree and angular cosine of experts'judgment information(order relation vectors). First, experts are classified by combined similarity degree using a clustering algorithm based on broad first searching neighbors. Then, a nonlinear programming is established to aggregate experts'judgments in each class with the purpose of minimizing the total judgment difference. Finally, all the aggregated judgments are integrated as the consensus of all experts. During this process, a group consensus is guaranteed by weights of individual expert and expert categories, which are dependent on the average similarity degree and the number of individual expert included in the class, respectively. This method could transform the complicated multi-expert group decision problem into low complexity “two-person” decision question. A numerical example shows the validity of the method.

Key words: group decision-making, judgment information, combined similarity degree, consensus, aggregation

中图分类号:

C934

孙晓东, 冯学钢. 群决策中基于判断相似度的专家聚类及群体意见集结方法[J]. 运筹与管理, 2014, 23(1): 51-58.

SUN Xiao-dong, FENG Xue-gang. Expert Classification and Aggregation Method for Group Decision-making Based on Judgment Similarity Degree[J]. Operations Research and Management Science, 2014, 23(1): 51-58.

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