序数偏好下多属性群决策的动态规划法  

Dynamic programming approach to multi-attribute group decision-making with ordinal preferences

作　　者：李武[1] 董峰[2] 陈妍[3] 

机构地区：[1]湖南理工学院信息与通信工程学院,河南郑州450006 [2]黄河科技学院现代教育技术中心,河南郑州450006 [3]湖南理工学院数学学院,湖南岳阳414006

出　　处：《华中科技大学学报（自然科学版）》2009年第10期48-51,共4页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家高技术研究发展计划资助项目(2009AA04Z107);国家自然科学基金资助项目(60774084);湖南省教育厅优秀青年项目(08B030);湖南理工学院科研基金资助项目(2008Y17)

摘　　要：对所有决策者均给出每个属性下备选方案的排序向量的决策问题,提出一种排序不一致性极小化方法.先考虑属性权重,以方案的综合排序与其在各属性下排序的加权不一致性最小为目标建立非线性整数规划模型,用动态规划求得各决策者对方案的综合排序.再将方案的群体排序与各个体排序的加权不一致性最小化,求得方案的最终排序结果.该方法将Cook-Seiford社会选择函数扩展到考虑属性及决策者权重的多属性群决策情形,可较好地避免排序结果的非惟一性.供应商选择算例及结果讨论表明了该方法的有效性.A method minimizing the unconsistency of ordinal preferences is proposed for a decision-making problem with rankings of alternatives given by decision makers in respect to each attribute.A nonlinear integer programming model minimizing the attribute-weighted unconsistency between the integrated rankings of the alternatives and the ones in respect to every attribute was developed and then transformed into a dynamic programming to obtain their integrated rankings for every decision maker.Similarly,their final rankings were determined when the decision maker-weighted unconsistency between their rankings for the group and the ones for every decision maker was minimized. This work extends the Cook-Seiford social selection function to multi-attribute group decision-making considering the weights of attributes and decision makers and can obtain unique ranking result. A supplier selection case illustrated the proposed method, and some discussions on the results verified its effectiveness.

关 键 词：多属性群决策 序数偏好 最小偏差法 动态规划 Cook-Seiford函数 

分 类 号：TP14[自动化与计算机技术—控制理论与控制工程] N945.25[自动化与计算机技术—控制科学与工程]