Improving discrimination in data envelopment analysis without losing information based on Renyi’s entropy

Data envelopment analysis (DEA) heavily depends on the dimensionality of the variables, and previous studies address the problem by decreasing the dimensionality with a minimal loss of information. Since the lost information can also have the impact on the evaluation performance, this paper accordingly proposes an approach to improve the discriminatory power of DEA without losing any variables information and without requiring any additional preferential information. Furthermore, an accelerating approach based on the concept of parallel computing is introduced to solve the multi-subsets problem. Listing all the possible variables subsets as the nodes, then the DEA efficiencies under each node are calculated, and the corresponding purity of information can be scientifically generated based on Renyi’s entropy. Subsequently, the important degrees of nodes are obtained by normalizing the purities of information, and the comprehensive efficiency scores can be finally generated by the weighted sum between the important degrees and the efficiencies under the corresponding node. Two specific examples are provided to evaluate the performance.