Choquet-Integral-Based Data Envelopment Analysis with Stochastic Multicriteria Acceptability Analysis

Data envelopment analysis (DEA) is a non-parametric method for measuring the efficiencies of decision-making units (DMUs) by using a set of inputs and a set of outputs. However, traditional DEA models always assume that the inputs or outputs are independent of each other, which is unrealistic in practical problems. To reflect the interactions between inputs or outputs, the Choquet integral is employed in DEA models. The traditional DEA models are usually used to find some specific input and output weights of DMUs to optimize the efficiency score of DMUs, but the corresponding input and output weights for the optimal efficiency score of a DMU may not be distributed symmetrically, that is to say, the space of weights may be different for different DMUs. Instead of finding the self-efficiency score and the cross-efficiency score of a DMU in traditional DEA models based on some specific input and output weights, stochastic multicriteria acceptability analysis is used to explore the input or output evaluation space and weight space to calculate the Choquet-integral-based acceptability indices of DMUs. The proposed method considers the interactions between inputs or outputs, which can make more DMUs efficient and can also measure the acceptability of a DMU to become an efficient one by exploring the supporting information space. Examples are given to illustrate the proposed method.