A hybrid DEA–fuzzy clustering approach for accurate reference set identification

This study integrates Data Envelopment Analysis (DEA) with Machine Learning (ML) to address key limitations of traditional DEA in identifying reference sets for inefficient Decision-Making Units (DMUs). In DEA, inefficient units are evaluated against benchmark units; however, some benchmarks may be inappropriate or even outliers, which can distort the efficiency frontier. Moreover, when a new DMU is added, the entire model must be recalculated, resulting in high computational costs for large datasets. To overcome these issues, we propose a hybrid approach that combines Fuzzy C-Means (FCM) and Possibilistic Fuzzy C-Means (PFCM) clustering. By leveraging Euclidean distance and membership degrees, the method identifies closer and more relevant reference units, while a sensitivity threshold is introduced to control the number of benchmarks according to practical requirements. The effectiveness of the proposed method is validated on two datasets: a banking dataset and a banknote authentication dataset with 1,372 samples. Results show that the reference sets derived from this ML-based framework achieve 71.6%–98.3% agreement with DEA, while overcoming two major drawbacks: (1) sensitivity to dataset size and (2) inclusion of inappropriate reference units. Furthermore, statistical analyses, including confidence intervals and McNemar’s test, confirm the robustness and practical significance of the findings.