A method to determine the integrated weights of cross-efficiency aggregation

Abstract

The cross-efficiency method is an effective way to rank decision-making units (DMUs) in data envelopment analysis. The traditional approach for cross-efficiency aggregation relies on an equally weighted average that ignores their relative importance. Although many aggregation methods based on prospect theory and Shannon entropy have been proposed by scholars, there are still some drawbacks in existing cross-efficiency aggregation approaches. First, the subjective weighting method based on prospect theory cannot reflect the preference of the decision maker (DM) in a more flexible way. Second, the determination of aggregation weights only considers a single perspective that may not comprehensively reflect the decision information. To address these deficiencies, this study proposes a new method for deriving meaningful aggregation weights from subjective and objective perspectives. From a subjective perspective, prospect theory is introduced to reflect the preference of DM, and this method provides an interval of reference point that is able to select such a reference point in light of the DMs’ preferences and decision goals. The idea of variance is then used to reflect the degree of deviation between peer-evaluation efficiency and self-evaluation efficiency, and objective weights are obtained. Moreover, an optimization model is constructed to obtain integrated weights that reflect both the subjective preference of the DM and the intrinsic objective information contained in the cross-efficiency matrix. Finally, two numerical examples are examined to illustrate the effectiveness and rationality of the proposed method.