Fuzzy Efficiency Estimates of the Turkish Health System: A Comparison of Interval, Bias-Corrected, and Fuzzy Data Envelopment Analysis

This study applies a multistep fuzzy stochastic procedure to evaluate Turkish health system efficiency by comparing crisp and stochastic efficiency estimates blending machine learning predictors. Conventional, biascorrected, and fuzzy data envelopment analysis (DEA) estimates are employed and compared to explore provincebased health systems' efficiency scores. Fuzzy DEA alevel models are used to assess underlying uncertainty, yielding fuzzy results by changing 10 different alpha (a)cut parameters from 0.10 to 1. Data are obtained from the official statistics of the Turkish Statistical Institute, and cross-province efficiency comparisons are performed through spatial analysis of the best and worst performers. A Pythagorean forest is constructed incorporating random forest regression to identify the most accurate predictors of province-based efficiency scores. The results reveal that bias correction and fuzziness outperform conventional efficiency analysis. High efficiency scores are observed when the a-cut parameter in the fuzzy DEA application is increased. High correlations are observed between efficiency scores elicited from crisp and stochastic DEA estimates (rs > 90). The spatial distribution of average fuzzy DEA scores (alpha = 1) for seven geographic regions are presented on a map of Turkey. Finally, considering the imprecision of the fuzzy DEA estimates, fuzzy DEA efficiency scores are used to identify the predictors of health system fuzzy efficiency scores. The Pythagorean forest demonstrates that the most important predictor of provincebased fuzzy efficiency scores is the number of physicians. The average efficiency values obtained from the conventional DEA model are outstanding in comparison to biascorrected and fuzzy DEA estimates. Future studies could compare crisp and fuzzy efficiency estimates using large spatial datasets.