A hybrid DEA–fuzzy clustering approach for accurate reference set identification
Sara Fanati Rashidi, Maryam Olfati, Seyedali Mirjalili, Crina Groşan, Jan Platoš, Václav Snåšel · Machine Learning with Applications · 2025
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.