Application of Neutrosophic Stratified Ranked Set Sampling: An Efficient Sampling Technique in the Estimation of Average Relative Humidity in USA

Abstract

The study examined the shortcomings of conventional statistical techniques in managing unclear or ambiguous data and emphasized the necessity of implementing neutrosophic statistical techniques as a more enhanced remedy. Advanced techniques like neutrosophic statistics (NS) were developed since traditional statistical methods are unable to handle the uncertainty present in ambiguous data. In order to tackle this problem, the study suggested an innovative and novel sampling method called "neutrosophic stratified ranked set sampling (NSRSS)" in addition to specialized neutrosophic estimators for precisely predicting the population mean in the proximity of uncertainty. This novel strategy adjusted ranked set sampling (RSS) techniques to allow the special features of neutrosophic data. Furthermore, the study improved the precision of estimating the population mean in uncertain situations by introducing neutrosophic estimators that use subsidiary information inside the structure of stratified ranked set sampling (SRSS). The work provided theoretical insights into the performance of these estimators by presenting comprehensive formulations of bias and mean squared error (MSE). To illustrate the efficacy of the suggested techniques, the study includes simulation studies, numerical examples conducted using the computer language R. Evaluations utilizing MSE, and percentage relative efficiency (PRE) demonstrated the higher accuracy of the suggested estimators over conventional alternatives. The findings demonstrated the NSRSS's applicability, particularly for predicting population means in situations where heterogeneity and uncertainty are prevalent. Furthermore, it was demonstrated that the estimators and technique produced interval-based findings, which provided a more accurate depiction of the uncertainty related to population parameters. The reliability of the estimators in estimating population means was greatly improved by this interval estimation in combination with a lower MSE. A significant vacuum in the field of statistical research is filled by the study's introduction of estimators and a customized sampling approach made especially for neutrosophic data. This research significantly advances statistical theory and practice by extending traditional statistical approaches to efficiently handle ambiguous data, especially for applications where exact data is few, heterogeneous, or uncertain. The empirical validation through numerical illustrations and simulations conducted in R further solidifies the practicality and robustness of the proposed techniques, reinforcing their applicability to real-world scenarios. © 2025, American Scientific Publishing Group (ASPG). All rights reserved.