A Hierarchical Clustering Approach Based on Three-Dimensional Gray Relational Analysis for Clustering a Large Group of Decision Makers with Double Information

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• 作者：Jianjun Zhu ; Shitao Zhang ; Ye Chen ; Lili Zhang
• 关键词：Group decision ; Double information ; Gray correlation degree ; Clustering center
• 刊名：Group Decision and Negotiation
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：25
• 期：2
• 页码：325-354
• 全文大小：1,179 KB
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• 作者单位：Jianjun Zhu (1)
  Shitao Zhang (1)
  Ye Chen (1)
  Lili Zhang (1)
  
  1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, Jiangsu, China
  
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Operation Research and Decision Theory
  Social Sciences
  
• 出版者：Springer Netherlands
• ISSN：1572-9907

文摘

Two types of information, collectively referred to as double information, are usually required in management decision-making. The first is preference information expressed in a judgment matrix. The second is reference information expressed in a multi-attribute decision matrix. In this paper, we investigate large-scale group clustering problems with double information in group decision-making. We first establish a novel three-dimensional gray correlation degree index, which integrates the alternative decision-making vector, index vector and alternative preference vector, to fully excavate the correlation between decision makers with double information. We then develop a new clustering procedure combining three-dimensional gray relational analysis and the concept of hierarchical clustering. Moreover, a model for determining clustering centers is established on the basis of the maximum gray correlation degree within each cluster and minimum gray correlation degree among clusters. A heuristic algorithm for the model to identify the core decision maker in each cluster is proposed. Finally, we illustrate the applications of the developed procedures with a practical case. The rationality of the proposed method is demonstrated by comparing results with results obtained using other methods, including the traditional gray clustering method and hierarchical clustering method with single information; i.e., preference information or reference information. Keywords Group decision Double information Gray correlation degree Clustering center