{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T03:54:33Z","timestamp":1778126073533,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,18]],"date-time":"2023-09-18T00:00:00Z","timestamp":1694995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["4235"],"award-info":[{"award-number":["4235"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>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\u2208[YL,YU] utilizing all the indeterminate values of the neutrosophic auxiliary variable XN\u2208[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.<\/jats:p>","DOI":"10.3390\/axioms12090890","type":"journal-article","created":{"date-parts":[[2023,9,19]],"date-time":"2023-09-19T03:02:17Z","timestamp":1695092537000},"page":"890","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Ratio-Type Estimator for Estimating the Neutrosophic Population Mean in Simple Random Sampling under Intuitionistic Fuzzy Cost Function"],"prefix":"10.3390","volume":"12","author":[{"given":"Atta","family":"Ullah","sequence":"first","affiliation":[{"name":"Department of Statistics, Quaid-i-Azam Univesity, Islamabad 45320, Pakistan"},{"name":"Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan"}]},{"given":"Javid","family":"Shabbir","sequence":"additional","affiliation":[{"name":"Department of Statistics, Quaid-i-Azam Univesity, Islamabad 45320, Pakistan"},{"name":"Department of Statistics, University of Wah, Wah Cantt 47040, Pakistan"}]},{"given":"Abdullah","family":"Alomair","sequence":"additional","affiliation":[{"name":"Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia"}]},{"given":"Mohammed","family":"Alomair","sequence":"additional","affiliation":[{"name":"Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,18]]},"reference":[{"key":"ref_1","unstructured":"Cochran, W.G. (1977). Sampling Techniques, John Wiley & Sons."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Singh, S. (2003). Advanced Sampling Theory with Applications: How Michael \u201cSelected\" Amy, Springer Science & Business Media.","DOI":"10.1007\/978-94-007-0789-4"},{"key":"ref_3","unstructured":"Singh, R., and Mangat, N.S. (2013). Elements of Survey Sampling, Springer Science & Business Media."},{"key":"ref_4","first-page":"159","article-title":"Ratio and product type exponential estimators","volume":"12","author":"Bahl","year":"1991","journal-title":"J. Inf. Optim. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.aml.2005.02.039","article-title":"Improvement in estimating the population mean in simple random sampling","volume":"19","author":"Kadilar","year":"2006","journal-title":"Appl. Math. Lett."},{"key":"ref_6","unstructured":"Singh, R., Chauhan, P., Sawan, N., and Smarandache, F. (2007). Auxiliary Information and a priori Values in Construction of Improved Estimators, Infinite Study."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1080\/02664760701835839","article-title":"On improvement in estimating the population mean in simple random sampling","volume":"35","author":"Gupta","year":"2008","journal-title":"J. Appl. Stat."},{"key":"ref_8","unstructured":"Al-Omari, A.I., Jemain, A.A., and Ibrahim, K. (2009). New ratio estimators of the mean using simple random sampling and ranked set sampling methods. Investig. Oper., 30."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1080\/15598608.2011.10412029","article-title":"Improved ratio and product exponential type estimators","volume":"5","author":"Upadhyaya","year":"2011","journal-title":"J. Stat. Theory Pract."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"782","DOI":"10.1080\/03610926.2011.579377","article-title":"Improved family of ratio estimators in simple and stratified random sampling","volume":"42","author":"Haq","year":"2013","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"199","DOI":"10.15446\/rce.v37n1.44366","article-title":"A new difference-cum-exponential type estimator of finite population mean in simple random sampling","volume":"37","author":"Shabbir","year":"2014","journal-title":"Rev. Colomb. Estad\u00cdStica"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3269","DOI":"10.1080\/03610926.2012.694547","article-title":"Improved ratio and product exponential type estimators for finite population mean in stratified random sampling","volume":"43","author":"Yadav","year":"2014","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0020-0255(75)90036-5","article-title":"The concept of a linguistic variable and its application to approximate reasoning\u2014I","volume":"8","author":"Zadeh","year":"1975","journal-title":"Inf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/0020-0255(75)90046-8","article-title":"The concept of a linguistic variable and its application to approximate reasoning\u2014II","volume":"8","author":"Zadeh","year":"1975","journal-title":"Inf. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1175","DOI":"10.1016\/j.ress.2005.11.017","article-title":"Survey of sampling-based methods for uncertainty and sensitivity analysis","volume":"91","author":"Helton","year":"2006","journal-title":"Reliab. Eng. Syst. Safety"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5955","DOI":"10.1016\/j.eswa.2008.07.087","article-title":"Fuzzy assessment method on sampling survey analysis","volume":"36","author":"Lin","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"7852","DOI":"10.1016\/j.eswa.2010.04.052","article-title":"Fuzzy assessment for sampling survey defuzzification by signed distance method","volume":"37","author":"Lin","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1142\/S0218488515400097","article-title":"An overview on the statistical central tendency for fuzzy data sets","volume":"23","author":"Sinova","year":"2015","journal-title":"Int. J. Uncertain. Fuzziness Knowl. Based Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1111\/tops.12172","article-title":"A sampling framework for uncertainty in individual environmental decisions","volume":"8","author":"Galesic","year":"2016","journal-title":"Top. Cogn. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.fss.2020.12.003","article-title":"Fuzzy importance sampling method for estimating failure possibility","volume":"424","author":"Feng","year":"2021","journal-title":"Fuzzy Sets Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"115602","DOI":"10.1016\/j.eswa.2021.115602","article-title":"Random sampling with fuzzy replacement","volume":"185","author":"Kesemen","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_23","unstructured":"Smarandache, F. (2013). Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability, Sitech & Education Publishing."},{"key":"ref_24","unstructured":"Smarandache, F. (2014). Introduction to Neutrosophic Statistics, Sitech & Education Publishing."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Aslam, M. (2018). A new sampling plan using neutrosophic process loss consideration. Symmetry, 10.","DOI":"10.3390\/sym10050132"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2991","DOI":"10.1007\/s40747-021-00439-1","article-title":"Neutrosophic ratio-type estimators for estimating the population mean","volume":"7","author":"Tahir","year":"2021","journal-title":"Complex Intell. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3359","DOI":"10.1134\/S1995080222140219","article-title":"Determination of Population Mean Using Neutrosophic, Exponential-Type Estimator","volume":"43","author":"Kumar","year":"2022","journal-title":"Lobachevskii J. Math."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1007\/s40314-022-01820-7","article-title":"Generalized estimator for computation of population mean under neutrosophic ranked set technique: An application to solar energy data","volume":"41","author":"Vishwakarma","year":"2022","journal-title":"Comput. Appl. Math."},{"key":"ref_29","unstructured":"Singh, R., Smarandache, F., and Mishra, R. (2023). Cognitive Intelligence with Neutrosophic Statistics in Bioinformatics, Elsevier."},{"key":"ref_30","first-page":"14","article-title":"Generalized Neutrosophic Sampling Strategy for Elevated estimation of Population Mean","volume":"53","author":"Yadav","year":"2023","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Alomair, A.M., and Shahzad, U. (2023). Neutrosophic Mean Estimation of Sensitive and Non-Sensitive Variables with Robust Hartley\u2013Ross-Type Estimators. 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