The results of CFNDEA approach: .

The measurement of productivity change in decision-making units (DMUs) is crucial for assessing their performance and supporting efficient decision-making processes. In this paper, we propose a new approach for measuring productivity change using the Malmquist productivity index (MPI) within the context of two-stage network data envelopment analysis (TSNDEA) under data uncertainty. The two-stage network structure represents a realistic model for DMUs in various fields, such as insurance companies, bank branches, and mutual funds. However, traditional DEA models do not adequately address the issue of data uncertainty, which can significantly impact the accuracy of productivity measurements. To address this limitation, we integrate the MPI methodology with an uncertain programming framework to tackle data uncertainty in the productivity change measurement process. Our proposed approach enables the evaluation of productivity change by capturing both technical efficiency and technological progress over time. By incorporating fuzzy mathematical programming into the DEA framework, we model the inherent uncertainty in input and output data more effectively, enhancing the robustness and reliability of productivity measurements. The utilization of the proposed approach provides decision-makers with a comprehensive analysis of productivity change in DMUs, allowing for better identification of efficiency improvements or potential areas for enhancement. The findings from our study can enhance the decision-making process and facilitate more informed resource allocation strategies in real-world applications.