Simulation and real-world applications of exponential–log estimators under neutrosophic ranked set sampling

In order to increase the effectiveness of population mean estimate under uncertainty, we provide a novel exponential–log type estimator in the context of neutrosophic ranked set sampling (NRSS). The neutrosophic strategy is appropriate for ambiguous real-world data because it can handle uncertain, inconsistent, and incomplete information. Compared to current neutrosophic estimators, the suggested estimator offers more flexibility and resilience by including both exponential and logarithmic transformation structures. We determine the circumstances in which the suggested estimator performs better than traditional estimators and extract the bias and mean squared error (MSE) expressions of the estimator under NRSS. The advantage of the suggested approach in terms of lower MSE and improved stability, especially when auxiliary information is inaccurate, is demonstrated by a comparative efficiency analysis substantiated by numerical demonstrations and simulation studies. The results demonstrate how complicated estimating issues under uncertainty may be addressed by combining neutrosophic sampling strategies with exponential-log forms.