DEA Cross-Efficiency Method for Ranking Units Based on Competitive vision

Ranking units which include multiple inputs and outputs in natural and social systems is a complex problem. DEA cross-efficiency evaluation method is an effective approach widely used in evaluating and ranking the decision making units to tackle this problem. The traditional cross-efficiency model is lack consideration for the relationships among DMUs. For this problem, the paper constructs the relationship matrix among DMUs to reflect the relationships among DMUs based on competitive interval and competitive vision. the paper start with calculating the efficiency interval based on benevolent and aggressive model, then adopt the ideas of competitive vision to design the competition level, cooperation level and competition-cooperation level coefficients .Thirdly, reconstruct the relation matrix of the DMUs on the basis of definitive efficiency interval using competition-cooperation level coefficient. Fourthly, introduce the relation matrix to cross-efficiency evaluation method for calculating efficient value and ranking DMUs. The method avoids the subjective factors caused by evaluators to accord with the actual situations of DMUs and use process information effectively. Finally, an illustrative example is provided to verify the rationality and validity of the proposed model.