基于格理论的数据包络分析方法

基于偏序集理论的数据包络分析方法中通过引进适当的偏序关系，不仅建立了决策单元之间的特殊关系，也给出了决策单元无效及弱有效的部分原因。然而，随着决策单元所选取投入产出指标个数的增加，决策单元之间的偏序关系可能越来越少，从而能为决策者提供的决策消息也随之减少。本文通过引进决策单元之间的交并运算生成了新的样本决策单元，这些决策单元与原有决策单元将构成格，且这一格关系不仅能够为决策单元的投影提供相关依据，也为决策单元的合作与竞争提供新了思路。最后，引进了相关定理、算法及实例。

Data envelopment analysis method based on lattice theory

With the introduction of proper partial order relation into the data envelopment analysis （DEA） method based on the partial ordered set theory, not only the relationships between different decision making units are established, but also some reasons which make the decision making units inefficient or weakly efficient are known. However, less information will be proposed for decision makers with the increase of the index number of input and output data which makes the relationships between different decision making units decrease. With the introduction of meet and join operations of decision making units, new sample decision making units are provided and the original decision making units and the provided sample decision making units compose a lattices. The lattice relation of decision making units not only proposes a new projection method but also a cooperation and competition method for decision makers. Some related theorems, algorithms and examples are provided.