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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 55 Issue: 2

Neutrosophic-based estimators for the population mean incorporating attribute information

Priya Priya(Central University of Haryana)0009-0001-2596-0935
Anoop Kumar(Central University of Haryana)0000-0003-2775-6548
Pages
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Publication Date
2026-02-18
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The developed framework thus provides a robust alternative for mean estimation when uncertain or imprecise attribute information is available.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the presence of indeterminate, inconsistent, or imprecise data, the conventional estimation procedures often fail to give reliable results.
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Key Findings & Data:A comprehensive simulation study, along with an empirical illustration on real-world data, demonstrates that the developed neutrosophic estimators consistently outperform the adapted neutrosophic estimators.
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Conclusion & Impact:The developed framework thus provides a robust alternative for mean estimation when uncertain or imprecise attribute information is available.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Auxiliary attribute · efficiency comparison · mean square error

Abstract

In the presence of indeterminate, inconsistent, or imprecise data, the conventional estimation procedures often fail to give reliable results. To address this limitation, the present study develops novel neutrosophic estimation procedures for the population mean by incorporating auxiliary attribute information under simple random sampling (SRS). The proposed approach extends the conventional attribute-based estimation procedures to the neutrosophic framework, where uncertainty, truthiness, and falsity are simultaneously represented. We adapted some prominent conventional estimators under neutrosophic environment and developed a new class of neutrosophic estimators with their properties, such as bias and mean square error (MSE) up to first-order approximation. Comparative efficiency analyses are conducted with respect to the adapted estimators to highlight the gain in precision achieved through the proposed estimators. A comprehensive simulation study, along with an empirical illustration on real-world data, demonstrates that the developed neutrosophic estimators consistently outperform the adapted neutrosophic estimators. The developed framework thus provides a robust alternative for mean estimation when uncertain or imprecise attribute information is available.

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Cite This Article

Priya, P., Kumar, A. (2026). Neutrosophic-based estimators for the population mean incorporating attribute information. Hacettepe Journal of Mathematics and Statistics, Volume: 55 Issue: 2. https://doi.org/10.15672/hujms.1825896

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References (39)

  1. V.D. Naik and P.C Gupta, A note on estimation of mean with known population proportion of an auxiliary character, Jour. Ind. Soc. Agr. Stat. 48 (2), 151-158, 1996.
  2. R. Singh, P. Chauhan, N. Sawan and F. Smarandache, Ratio estimators in simple random sampling using information on auxiliary attribute, Pak. J. Stat. Oper. Res. IV (1), 47-53, 2008.
  3. A.M. Abd-Elfattah, E.A. El-Sherpieny, S.M. Mohamed, and O.F. Abdou, Improvement in estimating the population mean in simple random sampling using information on auxiliary attribute, Appl. Math. Comput. 215, 4198–4202, 2010.
  4. L.K. Grover and P. Kaur, An improved exponential estimator of finite population mean in simple random sampling using an auxiliary attribute, Appl. Math. Comput. 218 (7), 3093-3099, 2011.
  5. E. Zamanzade and M. Mahdizadeh, A more efficient proportion estimator in ranked set sampling, Stat Prob Lett. 129, 28-33, 2017.
  6. E. Zamanzade and X. Wang, Proportion estimation in ranked set sampling in the presence of tie information, Comput. Stat. 33 (3), 1349-1366, 2018.
  7. E. Zamanzade and M. Mahdizadeh, Estimating the population proportion in pair ranked set sampling with application to air quality monitoring, J. Appl. Stat. 45 (3), 426-437, 2018.
  8. T. Zaman and C. Kadilar, Novel family of exponential estimators using information of auxiliary attribute, J. Stat. Manag. Syst. 22 (8), 1499-1509, 2019.
  9. T. Zaman, Generalized exponential estimators for the finite population mean, Stat. Transit. New Ser. 21 (1), 159-168, 2020.
  10. S. Bhushan and A. Kumar, Log type estimators of population mean under ranked set sampling, In Predictive Analytics using Statistics and Big Data: Concepts and Modeling, Bentham Science Publishers, 2020.
  11. E. Zamanzade and M. Mahdizadeh, Using ranked set sampling with extreme ranks in estimating the population proportion, Stat. Methods Med. Res. 29 (1), 165-177, 2020.
  12. S. Ahmad, E. Zahid, J. Shabbir, M. Aamir, W. Emam, Y. Tashkandy and S. Ahmad, A simulation study: An enhanced generalized class of estimators for estimation of population proportion using twofold auxiliary attribute, Heliyon 9 (6), e17269, 2023.
  13. H. E. Semary, S. Ahmad, I. Elbatal, C. Chesneau, M. Elgarhy and E. M. Almetwally, New comprehensive class of estimators for population proportion using auxiliary attribute: Simulation and an application, Alex. Eng. J. 99, 130-136, 2024.
  14. S. Ahmad and J. Shabbir, Proportion estimation using enhanced class of estimators under simple random sampling: Application with real data sets and simulation, Meas- Interdiscip. Res. 23 (3), 297-309, 2025.
  15. F. Smarandache, Neutrosophic set - a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math. 24, 287-297, 2005.
  16. Z. Tahir, H. Khan, M. Aslam, J. Shabbir, Y. Mahmood and F. Smarandache, Neutrosophic ratio-type estimators for estimating the population mean, Complex Intell. Syst., 7 (6), 2991-3001, 2021.
  17. S. Kumar, S.P. Kour, M. Choudhary and V. Sharma, Determination of population mean using neutrosophic exponential-type estimator, Lobachevskii J. Math. 43 (11), 3359-3367, 2022.
  18. S.K. Yadav and F. Smarandache, Generalized neutrosophic sampling strategy for elevated estimation of population mean, Neutrosophic Sets Syst. 53, 1-20, 2023.
  19. A.M. Alomair and U. Shahzad, Neutrosophic mean estimation of sensitive and nonsensitive variables with robust Hartley–Ross-Type estimators, Axioms 12 (6), 578, 2023.
  20. V.K. Yadav and S. Prasad, Neutrosophic estimators for estimating the population mean in survey sampling, Meas-Interdiscip. Res. 22 (4), 373-397, 2024.
  21. M.A. Alqudah, M. Zayed, M. Subzar and S.A. Wani, Neutrosophic robust ratio type estimator for estimating finite population mean, Heliyon 10 (8), 1-12, 2024.
  22. R. Singh, A. Kumari, F. Smarandache and S.N. Tiwari, Construction of almost unbiased estimator for population mean using neutrosophic information, Neutrosophic Sets Syst. 76 (1), 2024.
  23. S. Al-Marzouki and S. Ahmad, Developing a generalized class of estimators for estimation of population mean using neutrosophic approach, Eur. J. Pure Appl. Math. 18 (3), 6477-6477, 2025.
  24. S. Al-Marzouki and S. Ahmad, An enhanced class of estimators for the population mean using neutrosophic statistics: a case study of the Islamabad Stock Exchange, Eur. J. Pure Appl. Math. 18 (3), 6434-6434, 2025.
  25. A. Kumar and Priya, Efficient neutrosophic exponential estimators for accurate population mean estimation in simple random sampling, J. Fuzzy Ext. Appl. e214646, 2025.
  26. Priya and A. Kumar, Robust neutrosophic exponential estimators of population mean in the presence of uncertainty, Qual. Quant. 59, 3827–3850, 2025.
  27. A. Yadav, D.K. Yadav, S.K. Yadav and T. Zaman, A novel neutrosophic estimation method for handling uncertainty in population mean estimation, Qual. Quant., 1-26, 2025.
  28. V.K. Yadav and S. Prasad, Neutrosophic estimators in two-phase survey sampling, Neutrosophic Sets Syst. 61 (1), 29, 2023.
  29. A. Kumari, R. Singh and F. Smarandache, New modification of ranked set sampling for estimating population mean: neutrosophic median ranked set sampling with an application to demographic data, Int. J. Comput. Intell. Syst. 17 (1), 210, 2024.
  30. B. Khanna, Generalized regressed exponential estimator for estimation of mean under neutrosophic ranked set sampling, Natl. Acad. Sci. Lett. 47, 719–725, 2024.
  31. A. Kumar and V. Kumar, Estimating population mean of climate data via neutrosophic imputation in simple random sampling, Qual. Quant., 2025.
  32. A. Kumar and V. Kumar, Uncertainty based efficient neutrosophic imputation methods for population mean, Natl. Acad. Sci. Lett., 2025.
  33. A. Kumar and V. Kumar, Simulation based evaluation of neutrosophic exponential imputations of population mean using neutrosophic ranked set sampling, Frankl. Open 14, 100468, 2025.
  34. A. Kumar, Priya and A. M. Alomair, Efficient classes of estimators for estimating indeterminate population mean using neutrosophic ranked set sampling, AIMS Mathematics 10 (4), 8946-8964, 2025.
  35. V. Singh, R. Singh and A. Kumari, Application of neutrosophic stratified ranked set sampling: an efficient sampling technique in the estimation of average relative humidity in USA, Int. J. Neutrosophic Sci. 26 (3), 166-190, 2025.
  36. A. Kumari, A. Singh and V. Singh, Handling imprecise climate information: a neutrosophic generalized estimator under stratified ranked set sampling for population mean, Int. J. Math. Math. Sci. 2025, 1-23, 4935567, 2025.
  37. F. Smarandache, Introduction to neutrosophic statistics, Sitech & Education Publishing, 2014.
  38. G.O. Kadilar, A new exponential type estimator for the population mean in simple random sampling, J. Mod. Appl. Stat. Methods. 15 (2), 2016.
  39. S. Bhushan, A. Kumar, S. Singh and S.Kumar, An improved class of estimators of population mean under simple random sampling, The Philippine Statistician, 70 (1), 33-47, 2021.