Regret-rejoice two-stage multiplicative DEA models-driven cross-efficiency evaluation with probabilistic linguistic information *

As a powerful efficiency evaluation tool, cross-efficiency measurement in data envelopment analysis (DEA) has been proverbially concerned. However, most of existing studies on cross-efficiency fail to notice the internal processes of decision-making units (DMUs) and the psychological behaviors of decision makers (DMs) simultaneously. To overcome this limitation, this study investigates the rejoice-regret probabilistic linguistic multiplicative DEA cross-efficiency evaluation method for two-stage system. First, considering the increasingly complex decision-making environment, probabilistic linguistic term set is employed to express inputs and outputs information, and a probabilistic linguistic multiplicative DEA (PLMDEA) model is designed. Then, the regret theory is adopted to construct a regret-rejoice crossefficiency PLMDEA (RC-PLMDEA) model, in which the regret attitude of DMs is captured. Subsequently, as the internal process of each DMU is remarked, a regret-rejoice cross-efficiency two-stage PLMDEA (RCTS-PLMDEA) model is established. In the end, we provide an empirical application of evaluating commercial banks for examining the effectiveness and applicability of the designed method, and sensitive analysis and comparative analysis are also offered to highlight the merits and robustness of the constructed method.