Efficiency analysis in bi-level on fuzzy input and output

Abstract

To enhance the conventional framework of data envelope analysis (DEA), a novel hybrid bi-level model is proposed, integrating fuzzy logic with triangular fuzzy numbers to effectively address data uncertainty. This model innovatively departs from the traditional DEA’s ’black box’ approach by incorporating inter-organizational relationships and the internal dynamics of decision-making units (DMUs). Utilizing a modified Russell’s method, it provides a nuanced efficiency analysis in scenarios of ambiguous data. The study aims to enhance the accuracy and applicability of Data Envelopment Analysis in uncertain data environments. To achieve this, a novel hybrid bi-level model integrating fuzzy logic is presented. Validated through a case study involving 15 branches of a private Iranian bank, the model demonstrates improved accuracy in efficiency assessments and paves the way for future research in operational systems uncertainty management. The results indicated that, among the 15 branches of a private Iranian bank analyzed for the year 2022, branches 1, 10, and 11 demonstrated leader-level efficiency, while branch 3 exhibited follower-level efficiency, and branch 1 achieved overall efficiency. These branches attained an efficiency rating of $E^{++}$, signifying a high level of efficiency within the model’s parameters.