DEA cross-efficiency framework for efficiency evaluation with probabilistic linguistic term sets

Data envelopment analysis (DEA) is widely used in various practical problems as a general framework for efficiency-evaluation problems by containing the input-output data. With the increasingly complex factors in practice, portraying the uncertainty in problems is necessary for ensuring the reasonableness of results. As the probabilistic linguistic term set (PLTS) is a powerful tool for depicting uncertain information comprehensively, we aim to propose a DEA cross-efficiency framework for efficiency evaluation under probabilistic linguistic environment, which includes (1) defining the preference-based expectation function of a PLTS, (2) establishing the probabilistic linguistic DEA model, (3) developing an algorithm based on the dual form of the probabilistic linguistic DEA model, and (4) building the positive ideal-seeking cross-efficiency model. Furthermore, simulation tests are made to provide guidance for decision makers on the value assignment in practical efficiency-evaluation problems. A case study is conducted to verify the applicability of the proposed framework.