最小化序数偏好距离的多属性群决策

Minimizing ordinal preferences' distance to multi-attribute group decision-making

针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,提出一种排序距离极小化方法。先定义排序向量的距离测度函数,并证明其符合Cook-Seiford条件;再以方案的群体排序与各个体排序的加权距离最小为目标建立非线性整数规划模型,求得决策群体对方案在每个属性下的排序;类似地,将方案的综合排序与其在每个属性下的排序的加权距离最小化,解得方案的最终排序结果。供应商选择算例及结果讨论表明该方法的有效性。该方法将Cook-Seiford函数扩展到多属性群决策,可较好地避免排序结果的非唯一性。

A method minimizing ranking vectors＇ distances is proposed for a decision-making problem with ranking vectors of the alternatives given by decision makers in respect to each attribute considered.A distance function for ranking vectors is developed and proved to satisfy the conditions proposed by Cook and Seiford.Then a nonlinear integer programming model minimizing decision maker-weighted distance between the rankings of the alternatives for the group and the ones for every decision maker is developed and solved by an exhaust algorithm to obtain the rankings of the alternatives for the group in respect to each attribute.With attribute-weighted distance between the integrated rankings of the alternatives and the ones under every attribute being minimized,similarly,the final rankings of the alternatives for the group are determined.A supplier selection case is presented to illustrate the proposed method,and some discussions on the results verifies its effectiveness.This work extends Cook-Seiford social selection function to multi-attribute group decision-making,and can obtain a unique ranking result for a problem.