中文摘要：

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.

英文摘要：

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.