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

Abstract

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.

Keywords:

• Data envelopment analysis
• efficiency evaluation
• probabilistic linguistic term set
• cross-efficiency evaluation
• positive ideal decision-making unit

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This article was supported by the National Natural Science Foundation of China (Nos. 71771155, 72071135).