(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Point estimates have their limitations in survey sampling due to the fact that they provide just a single value for the parameter under study, which may vary between samples due to sampling errors. By producing interval estimates of the expected position of the parameter, the neutrosophic approach serves as a viable alternative in sampling theory. The neutrosophic approach optimizes the traditional strategy for effectively handling ambiguous data. To find the mean of the population using neutrosophic information we introduce a new family of estimators that incorporate additional information. Discovering the bias and mean square error is performed up to the first-order approximation. These estimators are ideal for data which is logical, confused, or ambiguous. This estimator is designed to make neutrosophic statistics (NS) in basic random sampling easier to understand. To better show the range of possible values for our population parameter, we show numerical findings for these estimators as intervals rather than single points. To further assess the efficiency of our proposed neutrosophic estimator, we utilize interval data and simulation derived from the Islamabad Stock Exchange (ISE).