Z-number network data envelopment analysis approach: A case study on the Iranian insurance industry

The main aim of this research is to present an innovative method known as fuzzy network data envelopment analysis (FNDEA) in order to assess the performance of network decision-making units (DMUs) that possess a two-stage structure while taking into account the uncertainty of data. To attain this goal, we utilize various methodologies including the non-cooperative game (leader-follower) NDEA method, the concept of Z-number, credibility theory, and chance-constrained programming (CCP) to develop a model for the fuzzy NDEA approach. The FNDEA approach offers several advantages, such as the linearity of the presented FNDEA models, the ability to rank two-stage DMUs in situations of ambiguity, the provision of a unique efficiency decomposition method in an uncertain environment, and the capability to handle Z-information. To demonstrate the applicability and effectiveness of the proposed approach, we implement the Z-number network data envelopment analysis (ZNDEA) approach in assessing the performance of Iranian private insurance companies. The results of this implementation reveal that the proposed ZNDEA method is suitable and effective for measuring and ranking insurance companies in situations where data ambiguity is present.