Optimized sampling strategy for estimating population mean under uncertainty using auxiliary attribute

In survey sampling, efficient estimation of population parameters under uncertainty remains an essential challenge, especially when auxiliary information is imprecise or incomplete. This article proposes an optimized strategy for estimating the population mean by incorporating auxiliary attributes, which are qualitative in nature, easily accessible, and strongly associated with the study variable. A novel class of neutrosophic estimators is constructed to improve estimation efficiency under uncertainty using simple random sampling (SRS). The statistical properties of the proposed estimators such as bias and mean square error (MSE) are determined using first-order approximations. The efficiency of the proposed estimators is theoretically examined and compared with the adapted estimators. The results demonstrate that the proposed neutrosophic estimators provide substantial efficiency gains over adapted estimators. An empirical study and a simulation study based on real datasets support the theoretical findings. The study emphasizes the practical usefulness of auxiliary attributes in enhancing the accuracy and reliability of population mean estimation under uncertainty.