Neutrosophic estimation of population mean under correlated measurement errors using simple random sampling

In survey sampling, the accurate estimation of the population mean is often compro- mised by two major challenges: uncertainty arising from incomplete, imprecise, or vague data and correlated measurement errors (CMEs) arising from systematic or interde- pendent inaccuracies in recorded values. The traditional estimation methods generally assume precise measurements and independent errors, making them unsuitable under such conditions. This study proposes a strong methodological framework that incorpo- rates methodologies to address both uncertainty and CMEs. By employing a combina- tion of neutrosophic theory with CME, we develop a neutrosophic estimation framework for the population mean estimation in simple random sampling (SRS) that maintain effeciency under uncertainty and CME. The theoretical properties of the proposed esti- mators are analysed and their performance is demonstrated through a simulation study and some real data applications. The findings confirm that jointly addressing uncertainty and CMEs provides more reliable estimates of the population mean, and enhancing the validity of statistical inferences in complex situations.