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

Author:

Ullah Atta12,Shabbir Javid13,Alomair Abdullah4,Alomair Mohammed4

Affiliation:

1. Department of Statistics, Quaid-i-Azam Univesity, Islamabad 45320, Pakistan

2. Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan

3. Department of Statistics, University of Wah, Wah Cantt 47040, Pakistan

4. Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia

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.

Funder

Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Reference31 articles.

1. Cochran, W.G. (1977). Sampling Techniques, John Wiley & Sons.

2. Singh, S. (2003). Advanced Sampling Theory with Applications: How Michael “Selected" Amy, Springer Science & Business Media.

3. Singh, R., and Mangat, N.S. (2013). Elements of Survey Sampling, Springer Science & Business Media.

4. Ratio and product type exponential estimators;Bahl;J. Inf. Optim. Sci.,1991

5. Improvement in estimating the population mean in simple random sampling;Kadilar;Appl. Math. Lett.,2006

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