序数偏好下多属性群决策的最小偏差法  

Minimum Deviation Method for Multi-attribute Group Decision-making with Ordinal Preferences

作　　者：李武[1] 陈妍[2] 郭观七[1] 

机构地区：[1]湖南理工学院信息与通信工程学院 [2]湖南理工学院数学学院

出　　处：《管理学报》2010年第5期781-784,共4页Chinese Journal of Management

基　　金：国家自然科学基金资助项目(60904059;60975049);国家高技术研究发展计划资助项目(2009AA04Z107);湖南省教育厅优秀青年资助项目(08B030)

摘　　要：对给出方案优先序的多属性群决策问题,考虑每个属性下各决策的权重,提出一种最小偏差法:以群体偏好与各个体偏好之间的加权偏差最小为目标建立非线性整数规划模型,并将其转化为指派问题求得方案在每个属性下的群体排序;以方案在每个属性下的排序与其综合排序的加权偏差最小为目标,解得方案的最终群体综合排序结果。该方法将Cook-Seiford函数扩展到多属性及考虑权重的情形,避免了排序结果的非唯一性。最后,以供应商选择算例说明其应用。A minimum deviation method is proposed for multi-attribute group decision-making problem with ordinal preference of alternatives given by decision makers and weights of them with respect to each attribute.A nonlinear integer programming model minimizing the weighted deviations between the group＇s ordinal preferences and all individual ones of the alternatives under each attribute is developed and transformed to an assignment problem to obtain the group＇s rankings of the alternatives under each attribute.The final integrated rankings of the alternatives in the group＇s opinion are derived similarly.The proposed method extends the Cook-Seiford social selection function to decision-making with multi-attribute and experts＇ weights,and can obtain unique ranking result.A supplier selection example is presented to illustrate the method.

关 键 词：多属性群决策 序数偏好 最小偏差法 Cook-Seiford社会选择函数 供应商选择 

分 类 号：C934[经济管理—管理学] N945.25[自然科学总论—系统科学]