基于聚类的多属性群决策专家权重确定方法

A Method for Determining the Experts' Weights of Multi-Attribute Group Decision-Making Based on Clustering Analysis

对于多属性群决策中专家权重确定的问题,本文提出了基于聚类的专家权重确定方法,将专家权重分为类别间权重和类别内权重,对专家聚类步骤和类别间权重的计算方法进行了改进。通过专家给出的判断矩阵构建相容度矩阵,利用系统聚类原理,对相容度矩阵进行聚类,得到最大相容度谱系图。通过最大相容度间的距离和给定阈值的比较,对专家进行恰当分类,从而避免了根据现有研究步骤只能将专家分为两类的不足。此外,在确定类别间权重时,除继续对类容量较大的类赋予较大的类别间权重系数外,还引入专家判断矩阵的属性权重一致性来反映类别间的差异,从而有效避免了当某几类专家中含有相等数目专家时,赋予这几类专家相同类别间权重系数的问题。所提方法结构清晰、计算简便,并使得专家权重计算结果更为合理准确。最后运用一个算例对比验证了该方法的可行性和有效性。

An experts’ weight determining method based on the experts ’ weights clustering analysis is proposed to determine the experts’ weights of multi-attribute group decision-making.The experts’ weight is divided into the weights between categories and within category .The steps of experts ’ clustering and the calculation method of the weights between categories are improved .The clustering pedigree chart of the maximum compatibility de-gree is got by building the expert judgment compatibility matrix according to the expert judgment matrix , making use of the system clustering principle to cluster the compatibility degree matrix .The experts are classified proper-ly according to the comparison of the distance between the maximum compatibility degree and the given threshold value, which overcomes the shortcoming of only clustering the experts into two categories in existing literatures . In addition, while determining the weights between categories , it not only gives greater weight for the larger ca-pacity , but also reflects the difference between categories by introducing the attribute ’ s weight consistence of the experts ’ judgment matrix , which avoids giving the same weights between categories for those categories that have the same number experts .The structure of the proposed method is clear and the calculation is simple , which makes the final result of experts ’ weights more reasonable and accurate .Finally, an example is compared to val-idate the feasibility and effectiveness of the presented method .