Neutrosophic Ranked Set Sampling Scheme for Estimating Population Mean: An Application to Demographic Data

Abstract

The primary goal of this study is to address the limitations of classical statistics in handling am
biguous or indeterminate data. The best alternative to classical and fuzzy statistics for handling such data
 uncertainty is neutrosophic statistics, which is a generalization of both. A generalization of classical statistics,
 neutrosophic statistics addresses hazy, ambiguous, and unclear information. To achieve this, this manuscript
 recommends the neutrosophic ranked set sampling approach. We have introduced neutrosophic estimators for
 estimating the mean of the finite population using auxiliary information under neutrosophic ranked set sampling
 to address the challenges of estimation of the population mean of neutrosophic data. The proposed estimators
 outperform the other existing estimators and proposed estimators evaluated in this work using MSE and PRE
 criteria, and equations for bias and mean squared error produced for the suggested estimators up to the first
 order of approximation. Under neutrosophic ranked set sampling, the suggested estimator has demonstrated
 superiority over the class of estimators, unbiased estimators, and comparable estimators. Using the R pro
gramming language, a numerical illustration and a simulation study have been conducted to demonstrate the
 effectiveness of the suggested methodology. When computing results when working with ambiguous, hazy, and
 neutrosophic-type data, the provided estimators are particularly helpful. These estimators produce findings that
 are not single-valued but rather have an interval form where our population parameter may lie more frequently.
 Since we now have an estimated interval with the population mean’s unknown value provided a minimum MSE,
 the estimators are more effective

DOI: 10.5281/zenodo.11479519