In this work, an extended evaluation approach for decision making units (DMUs) with
a single output is proposed. Firstly, the input and output data for each DMU are
changed in the same proportion until all the outputs are equal, and then the
coordinate system is established with input i as the ith coordinate axis. Secondly, in
the coordinate system, the production possibility set, which is spanned by all the
DMUs without the evaluated DMU, is expressed by inequalities. Moreover, the
mathematical expression of the line segment joining the origin to the evaluated DMU
is given. Thirdly, the efficiency measure of the evaluated DMU is obtained from the
relationship between the production possibility set and the line segment. In order to
distinguish the weak efficiency and efficiency, the partially ordered set and minimal
element are introduced in the paper. Finally, an example is provided to illustrate the
proposed approach.

• An extended inequality approach for evaluating decision making units with a single output