Fuzzy set theory has significant and dominant applications in Taiwan’s insurance industry, especially in fields involving decision-making, uncertainty, and risk assessment. Providing the complexity and problems in assessing factors, for instance, natural disaster risks, customer creditworthiness, or health conditions, traditional binary logic often falls short. Taiwanese insurers have adopted fuzzy logic systems to enhance fraud detection, premium pricing, and privilege evaluations by catching the indistinctness characteristic in human ruling and imperfect data. The Taiwan insurance industry is a dynamic and spirited module of the commercial sector, contributing meaningfully to risk management and economic stability. For this, we study to propose an assessment of the proficiency of insurance enterprises using Network Data Envelopment Analysis. Toward this end, the frank operational laws for circular Pythagorean fuzzy (CPF) uncertainty are applied. Moreover, the CPF Choquet Frank averaging (CPFCFA) operator and CPF Choquet Frank geometric (CPFCFG) operator with three dominant properties for each operator have been studied. The study deliberates the multi-attributive border approximation area comparison (MABAC) model and verifies it with the help of numerical examples. This study enhances the industry’s efficiency to offer adapted insurance products and handle risks precisely, aligning with Taiwan’s push toward intelligent financial services and digital transformation. In the following, we establish the decision-making performance for assessing the proficiency of insurance enterprises using the network data envelopment analysis (NDEA) technique. Finally, we examine the ranking values of offered representations to compare them with the ranking values of prevailing models to show the capability and efficacy of the originated approaches.