Environmental efficiency evaluation with left–right fuzzy numbers

Undesirable outputs such as waste and smoke pollution are often produced along with desirable outputs in the production processes of many enterprises. Therefore, when evaluating production efficiency, both desirable and undesirable outputs should be considered simultaneously. Based on the previous data envelopment analysis model, we present a fuzzy slacks-based measure model incorporating a confidence coefficient on the postulation that inputs and outputs are left–right (L–R) fuzzy numbers. In this paper, the model not only solves the input slacks when presetting the confidence coefficient but also solves efficiency evaluation problems when undesirable output exists, thereby expanding the range of applications for environmental efficiency evaluation. Furthermore, it provides a basis for decision making in a wider range of situations to reduce undesirable outputs, control the quantities of pollutants discharged, and improve the environment. To provide an example of this last point, the proposed model is applied to perform an analysis of the industrial environmental performance of 31 provinces in China.