4. Linear monotonic decreasing transformation: This approach has been suggested by Seiford and Zhu (2002). Here, the data transformation is given by f(uik)=−uik+βi, where βi is a sufficiently large positive scalar. Lu and Lo (2007b) utilized this model to examine the overall performance of different regions in China, based on economic and environmental factors. In their analysis, the desirable output under consideration was GDP and the undesirable outputs were emissions such as soot, dust and sulphur dioxide. This model has been criticized for its invariance to data transformation within the DEA model (Lu and Lo, 2007a, 2007b).