Efficiency measurement of the water recycling system in a fuzzy environment

Assessing the water resource system from a circular economic perspective is essential for sustainable environmental development. In this study, a water recycling system, which consists of both water utilization and wastewater treatment processes with a closed-loop feedback cycle, is introduced. To evaluate the water recycling system with imprecise data, a fuzzy game cross-efficiency network data envelopment analysis model is developed. The proposed approach employs peer evaluation and considers the competitive relationship between decision-making units, enabling a more discriminatory power for evaluation. An application of the proposed approach to assess the water resource management performance of European Union countries is investigated. Our results show that the water utilization efficiency has a major impact on the overall system efficiency. Additional validation and sensitivity analysis are implemented to recognize the sources of inefficiency. Further recommendations are included to improve the efficiency of each process. A comparison between the proposed method and other studies is also presented to demonstrate the superiority of the proposed method.