在多属性群决策方法的研究中,为了科学地确定专家的权重,提出一种基于信息熵的群组聚类组合赋权法。依据各个专家的判断矩阵归一化得到的排序向量,利用相关系数法构造相关矩阵。通过分析阀值变化率选取最优聚类阀值,对相似程度较高的排序向量给出合理的聚类。运用信息熵为类内专家赋权,综合聚类结果和排序向量的信息熵,确定专家的总权重。算例表明该方法可以对较为相近的专家评价结果进行有效分类,并准确衡量每位专家评价信息量的大小,能够有效提高专家赋权的合理性和群组决策的科学性。
In terms of the research of multi-attribute group decision-making, a method for combination weighting experts is put forward based on information entropy and cluster analysis so as to scientifically determine the weight of every expert. According to the experts' collating vectors obtained by normalization of corresponding judgment matrixes, correlation matrix is constructed by the correlation coefficient. Through the analysis of change rate of threshold, the optimal clustering threshold is selected and the higher priority vector similarity obtained the reasonable clustering. The experts' weight of within-class can be ascertained by the theory of information entropy weight. The experts' weights are determined according to the result of classification and information entropy of collating vectors. Finally, a numerical example shows that the method is effective for the higher priority vector similarity classification and can accurately weighing every experts' information. The method will effectively improve the rationality of determining experts' weight and contribute to scientific group decision-making.
[1] 孙晓东, 田澎. 群决策中基于一致性强度的专家意见集结方法[J]. 系统工程与电子技术, 2008,30(10): 1895-1898.
[2] Bolloju N.Aggregation of analytic hierarchy process models based on similarities in decision makers' preferences[J].European Journal of Operational Research, 2001,128(3):499-508
[3] Herrera F,Herrera-Viedma E,Verdegay J L, Linguistic measures based on fuzzy concincidence for reaching consensus in group decision making[J]. International Journal of Approximate Reasoning, 1997,16(3-4):309-334.
[4] 江文奇,华中生.一种决策中决者判断一致性的聚类方法[J]. 中国管理科学,2005,13(2):35-39
[5] 李闯, 端木京顺, 蔡忠义, 等. 基于判断矩阵的模糊核专家聚类组合赋权方法[J]. 控制与决策, 2012,27(9):1411-1414.
[6] 高阳,罗贤新,胡颖.基于判断矩阵的专家聚类赋权研究[J].系统工程与电子技术,2009.31(3):593-596.
[7] Zhou Xuan,Zhang Fengming,Hui Xiaobin,et al. Group decision-making method based onentropy and experts cluster analysis[J]. Journal of Systems Engineering and Electronics,2011, 22( 3):468-472.
[8] Zhang Zhigang. An approach to multiple attribute group decision making for supplier selection[C]. Proceedings of IEEE International Conference on Advanced Management Science,Chengdu,China,July 9-11,2010.
[9] Ma LiYi, Xue Wanxin, Ge Jian. Entropy method for decision-making of fuzzy information[C]. Proceedings of 2010 IEEE International Conference on Advanced Management Science, Chengdu,China,July 9-11,2010.
[10] 陈水利,李敬公,王向功. 模糊集理论及其应用[M]. 北京:科学出版社,2005.
[11] 傅祖芸. 信息论[M]. 第三版.北京: 电子工业出版社, 2011.
[12] 刘立柱.概率与模糊信息论及其应用[M].北京:国防工业出版社,2005.
