Robust neutrosophic exponential estimators of population mean in the presence of uncertainty

One of the main goals of survey sampling is to estimate the population mean accurately, especially when working with uncertain data. In such situations, the traditional estimators frequently fail to retain robustness and accuracy, which calls for the development of more advanced estimation procedures. This study presents the robust neutrosophic exponential estimator to estimate the population mean under uncertainty employing simple random sampling (SRS). The suggested methods efficiently handle uncertain, inconsistent, and partial data by fusing the concepts of neutrosophy with the exponential estimators. We show through in-depth algebraic comparisons, simulation experiments, and real data illustrations that the proposed neutrosophic estimators not only improves robustness of the estimates but also offers improved accuracy in terms of least mean square error (MSE) and highest percent relative efficiency (PRE), when compared to the existing neutrosophic estimators namely, neutrosophic sample mean $$\bar{y}_N$$ y ¯ N , neutrosophic ratio estimator $$t_{r_N}$$ t r N , neutrosophic generalized ratio estimator $$t_{g_N}$$ t g N , neutrosophic regression estimator $$t_{lr_N}$$ t l r N , neutrosophic power ratio estimator $$t_{s_N}$$ t s N , neutrosophic exponential ratio estimator $$t_{bt_N}$$ t b t N , Tahir et al. (Complex Intell. Syst., 2021. https://doi.org/10.1007/s40747-021-521-00439-1 ) estimator $$t_{t_N}$$ t t N , Yadav and Smarandache (Neutrosophic Sets Syst. 53, 1-20, 2023) estimator $$t_{y_N}$$ t y N , and Yadav and Prasad (Interdiscip. Res. Perspect., 2024. https://doi.org/10.1080/15366367.2023.2267835 ) estimator $$t_{v_N}$$ t v N , particularly for datasets with high degrees of uncertainty. The results of this study provide a more trustworthy tool for survey practitioners working with uncertain data, and they have important implications for statistical techniques across different domains.