A cross-efficiency fuzzy Data Envelopment Analysis technique for performance evaluation of Decision Making Units under uncertainty

The paper presents a novel cross-efficiency fuzzy Data Envelopment Analysis (DEA) technique for evaluating different elements (Decision Making Units or DMUs) under uncertainty. In order to evaluate the performance of several DMUs while dealing with uncertain input and output data, the presented technique employs triangular fuzzy numbers. A fuzzy triangular efficiency is associated to each DMU through a cross evaluation obtained by a compromise between suitably chosen objectives. Results are then defuzzified to provide a ranking of the DMUs. The proposed method is applied to the performance evaluation of healthcare systems in a region of Southern Italy. The DMU data uncertainty derives from ongoing reforms and the reported assessment is conducted firstly in order to evaluate and rank the efficiency of the considered healthcare systems, and subsequently to assess the evolution of the performance of one of the most affected among these DMUs by the reform plans. The case study demonstrates the model ease of application, its discriminative power among DMUs when compared to a more classical fuzzy DEA approach, and the usefulness in planning and validating targeted reforms in the case of healthcare systems.