A Novel Approach for Efficiency Evaluation in Data Envelopment Analysis Framework with Fuzzy Stochastic Variables

Abstract

Data envelopment analysis (DEA) is a widely used approach for evaluating the relative efficiency of decision-making units (DMUs) in multiple-input and multiple-output situations. Although traditional DEA models use precise input–output data, real-world problems often involve mixed uncertainties, including fuzziness and stochasticity. This paper focuses on dealing with situations where inputs and outputs have both fuzzy and stochastic characteristics, using DEA models for efficiency evaluation. Through the integration of the α-level approach and chance-constrained programming, novel DEA models with fuzzy stochastic variables (FSVs) are proposed, and deterministic equivalent interval DEA models with linear constraints are provided to address this problem. The main contributions and advantages of the proposed model over existing DEA models with FSVs are fourfold: (1) linear and always-feasible models are proposed; (2) a fixed and uniform production boundary (i.e., the same set of constraints) is used to measure the efficiency of DMUs with fuzzy stochastic input and output; (3) the obtained results can distinguish between efficient and inefficient DMUs; (4) Equivalent interval DEA models were obtained to provide a more comprehensive assessment of the efficiency of the DMUs. Finally, a numerical example is presented to demonstrate the applicability of the proposed models and the feasibility of the obtained solutions.