Ratio-Type Estimator for Estimating the Neutrosophic Population Mean in Simple Random Sampling under Intuitionistic Fuzzy Cost Function

Abstract

Survey sampling has a wide range of applications in biomedical, meteorological, stock exchange, marketing, and agricultural research based on data collected through sample surveys or experimentation. The collected set of information may have a fuzzy nature, be indeterminate, and be summarized by a fuzzy number rather than a crisp value. The neutrosophic statistics, a generalization of fuzzy statistics and classical statistics, deals with the data that have some degree of indeterminacy, imprecision, and fuzziness. In this article, we introduce a fuzzy decision-making approach for deciding a sample size under a fuzzy measurement cost modeled by an intuitionistic fuzzy cost function. Our research introduces neutrosophic ratio-type estimators for estimating the population mean of the neutrosophic study variable YN∈[YL,YU] utilizing all the indeterminate values of the neutrosophic auxiliary variable XN∈[XL,XU] rather than only the extreme values XL and XU. Three simulation studies are carried out to explain the proposed methods of parameter estimation, sample size determination, and efficiency comparison. The results reveal that the proposed neutrosophic class of estimators produces more accurate and precise estimates of the neutrosophic population mean than the existing neutrosophic estimators in simple random sampling, which is the ultimate goal of inferential statistics.

Compromise optimum allocation in neutrosophic multi-character survey under stratified random sampling using neutrosophic fuzzy programming

“…Vishwakarma and Singh [35] investigated the neutrosophic estimator of a finite population mean in rank set sampling. Ullah et al [33] developed the ratio-type estimator for estimating the imprecise population mean and suggested the sample size estimation procedure in simple random sampling under fuzzy uncertainty. The stratified sampling design produces more efficient results than simple random sampling for heterogeneous study population and is widely used in agricultural, marketing, spatial, biomedical, and meteorological studies.…”