A flexible cross-efficiency model with partial preference for efficiency evaluation of clean transportation energy

The rapid development of the transportation industry benefits from the consumption of energy, but the excessive dependence on petroleum fuels makes it a major source of air pollution. In order to achieve green and high-quality development of the transportation industry, many countries are committed to scientifically evaluating the utilization efficiency of clean energy, which has attracted wide attention from the whole society. Significantly, without considering the diversity and complexity of pollutants, indicators used in previous studies were unable to cover all pollutants when establishing the evaluation index system. Meanwhile, as an efficient tool, data envelopment analysis (DEA) is extensively used when it comes to efficiency evaluation. However, the absolute preference of existing benevolent and aggressive cross-efficiency models limits its application scenarios. To address the challenges above, an improved flexible cross-efficiency DEA model is proposed considering both same and different benevolence coefficients of decision-making units (DMUs) on the basis of pointing out the inadequacy of the previous model. The concepts of consensus coefficient and group preference are introduced in the aggregation of cross-efficiency. Besides, based on the theory of undesirable output, the consumption of nonclean energy is taken into account as the input indicator to characterize the degree of pollution. The results show that the obtained cross-efficiency value and efficiency ranking of clean transportation energy change sensitively under various benevolent coefficients. There is an important practical significance to consider the independent preference information of DMUs for the evaluation and ranking of cross-efficiency.