基于偏序集理论的数据包络分析方法

Data envelopment analysis method based on poset theory

数据包络分析(data envelopment analysis,DEA)方法与偏序集理论之间关系密切,通过引入适当的偏序关系可以进一步刻画决策单元,也能够更加深入地理解决策单元。在Charnes-Cooper-Rhoes(C2 R)模型中引入新的偏序关系,通过该偏序关系给出DEA有效决策单元、弱有效决策单元及无效决策单元与偏序集的极大元的特殊关系,同时从偏序集中的极大元出发提供决策单元在生产前沿面上的投影。最后,为了较简单地确定各个决策单元之间的偏序关系,对C2 R模型中的投入产出数据进行无量纲化及统一化处理,并对这些理论的进一步应用和发展提出了一些建议和设想。

As the data envelopment analysis （DEA） method has close connection with the poset theory, theintroduction of proper partial order relation can further depict decision making units and provide a great help for a better understanding of them. With the introduction of new partial order relation into Charnes-Cooper-Rhoes（C2R） model, the special relationship between DEA efficient, weakly efficient, decision making units and the poset theory is revealed. Furthermore, through the introduced poset, a poset theory-based projection methodfor the decision making units is provided. Finally, to confirm the partial order relation of decision making units in C2R model, the non-dimensional processing and unified methods for input-output data are proposed. Some recommendationsand hypotheses for the further application and development of these theories are given.