Neutrosophic developments in Horvitz-Thompson type estimators

In the realm of unequal probability sampling and Horvitz-Thompson type technique, addressing the challenge of estimating the mean in the presence of ambiguous data is one of the most important topics that has not yet been thoroughly discussed. The presence of ambiguous data not only complicates the estimation process but also affects its sensitivity, particularly when dealing with variables of varying significance. Leveraging auxiliary information becomes crucial to mitigate these challenges. This study presents a pioneering method that combines neutrosophic statistics, Horvitz-Thompson type estimators employing unequal probability sampling for mean estimation, and the integration of auxiliary information. Neutrosophic set theory, extending classical set theory to manage indeterminacy, offers a framework for addressing inherent uncertainties within the data. By merging neutrosophic statistics with the Horvitz-Thompson technique, the study develops innovative mean estimators adept at effectively managing ambiguous data within unequal probability sampling. To assess the effectiveness of this approach, the study conducts a numerical analysis utilizing real-world data. Findings from this analysis showcase the superior efficiency of the proposed methodology.