Pareto approach for DEA cross efficiency evaluation based on interval programming

Efficiency assessment by using data envelopment analysis (DEA) in interval environment is studied. Two parameters with regard to the input and output are introduced to characterize the variability of the production possibility sets. The extended production facets with different production possibility sets are determined. The inclusion relation between different extended production facets is discussed, and self-evaluation models are constructed to calculate the interval efficiency of the decisionmaking units (DMUs) with the optimal production facet. By setting self-evaluation as a target, the aggressive and benevolent cross-efficiency models are established based on the likelihood between the values of self-evaluation and peer evaluation. The analysis of the models yields the interval cross-efficiency matrices and the weight allocation method that is more advantageous to the DMU for aggregating the interval cross-efficiency matrices. An example is used to illustrate the applications of the models.