On characterizations of weak data envelopment analysis-efficient units

There is a close relationship between a weakly efficient unit in DEA and a maximum element. On the basis of the theory of partially ordered sets, some characteristic properties of weak DEA efficiency on four DEA models are given in this paper. At the same time, the meaning of weak DEA efficiency is explained. In addition, the effects upon weak DEA efficiency due to the structure change of possible productive collections are discussed by using the theory on partially ordered set. At last, this paper discusses some problems on properties of data transformation, effects upon weak DEA efficiency due to the change of the numbers of DMUs or evaluated indexes and the relationships between models.