偏序集理论在数据包络分析中的应用研究

Using theory of partially ordered sets to study data envelopment analysis

DEA有效单元与偏序集的极大元之间关系密切 ,从偏序集的理论出发刻画了几种典型的 DEA模型所描述的 DEA有效单元的本质特征 ,并就 C2 R,C2 GS2 模型分析了 DEA有效前沿面的构成 ,证明了可能集中相对有效点与偏序集的极大元之间的一一对应关系 .进而对 DEA有效性的含义、DEA模型选取的基本原则等问题给出了基于偏序集理论的解释 .同时 ,讨论了可能集结构变化对 DEA有效性的影响 ,给出了刻画各可能集间关系的一些结论 .

It has close relationship between an efficient unit and a maximum element. On the basis of the theory of partially ordered sets, this paper gives some characteristic properties of effective units in several DEA models and analyses the structure of fronters in C 2R, C 2GS 2 models, then proves exiting the one to one correspondence between an effective point and a maximum element. At the same time, the meaning of DEA efficiency is explained and a basic rule of selecting models is provided. In addition, the effects upon DEA efficiency due to the structure change of possible productive collections are discussed and some results are given. Finally, some suggestions for future research are provided.