Integrating neutrosophic logic with ratio–Product methods: a novel estimator class for finite population mean

Real-world data typically have indeterminacy, uncertainty, and ambiguity, rendering classical statistical methods unreliable for inference. A flexible solution for addressing imprecise information is the neutrosophic framework. Estimation methods for crisp data are well-established, although neutrosophic estimators are still being developed. This paper introduces a novel exponential log-type ratio-cum-product estimator and a broader class of estimators for finite population mean estimation with uncertain and indeterminate data. Under the first-order approximation, we develop formulas for bias and mean squared error (MSE) and evaluate the suggested estimators' efficiency using percentage relative efficiency. Real temperature and medical data show that the method is effective in uncertain conditions. A thorough simulation investigation confirms the theoretical findings. Empirical and simulation results show that the suggested estimators have lower MSE and greater PRE than classical and existing neutrosophic estimators, establishing their superiority for real-world uncertain data analysis.