Abstract: The efficiency evaluation based on double frontier is introduced to traditional cross-efficiency model. At the same time, in view of the fact that decision makers cannot determine whether to choose an aggressive or a benevolent strategy and the limited application of these two cross-efficiency strategies, a new cross-efficiency method based on double frontier is proposed. The basic idea of this method is to select an ideal decision making unit (IDMU) and an anti-ideal decision making unit (ADMU), and the input and output weights of the evaluated decision making unit (DMU) are used to calculate the efficiencies of IDMU and ADMU. And then making the efficiency of each evaluated DMU as close to the efficiency of IDMU as possible and as far away from the efficiency of ADMU as possible simultaneously. According to the idea, the cross-efficiency value is solved and aggregated under the optimistic frontier and the pessimistic frontier respectively, which avoids the difference caused by the different choices of frontiers and the difficulty of decision makers to choose between benevolent and aggressive cross-efficient strategies. Finally, the proposed method is compared with the existing methods to valid its effectiveness, and the model is applied to the evaluation of innovation efficiency in eastern China.

Key words: data envelopment analysis; cross-efficiency strategy; data envelopment analysis based on double frontier; evaluation of innovation efficiency