Neutrosophic Method for Identifying Extreme Values in Imprecise Data Using Median Absolute Deviation

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DOI: https://doi.org/10.28924/2291-8639-23-2025-144
Published: Jun 16, 2025
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Muhammad Saleem, Muhammad Aslam, Neutrosophic Method for Identifying Extreme Values in Imprecise Data Using Median Absolute Deviation, Int. J. Anal. Appl., 23 (2025), 144.

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Muhammad Saleem, Muhammad Aslam

Abstract

The traditional calculation of Z-scores for outlier detection is highly sensitive to extreme data points, making it unsuitable under conditions of uncertainty. In this study, we propose a novel approach to modify the Z-score method using neutrosophic statistics. Key statistical measures, including the median, neutrosophic standard deviation, and median absolute deviation, will be computed based on neutrosophic random variables. An extensive simulation study will evaluate the impact of varying uncertainty levels on the adaptation of Z-scores for outlier detection and their effectiveness in identifying outliers. Comparative analysis of Z-scores derived from different methods will also be performed. The proposed methodology will be applied to neutrosophic GG25 gray cast iron data, demonstrating its practical utility. We hypothesize that uncertainty levels will significantly affect Z-score computations and, consequently, outlier detection in the dataset.

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References

  1. B. Iglewicz, D.C. Hoaglin, How to Detect and Handle Outliers, ASQC Quality Press, Milwaukee, 1993.
  2. V. Hodge, J. Austin, A Survey of Outlier Detection Methodologies, Artif. Intell. Rev. 22 (2004), 85-126. https://doi.org/10.1023/b:aire.0000045502.10941.a9.
  3. P. Venkataanusha, C. Anuradha, P.S.R.C. Murty, S.K. Chebrolu, Detecting Outliers in High Dimensional Data Sets Using Z-Score Methodology, Int. J. Innov. Technol. Explor. Eng. 9 (2019), 48–53. https://doi.org/10.35940/ijitee.A3910.119119.
  4. V. Aggarwal, V. Gupta, P. Singh, K. Sharma, N. Sharma, Detection of Spatial Outlier by Using Improved Z-Score Test, in: 2019 3rd International Conference on Trends in Electronics and Informatics (ICOEI), IEEE, Tirunelveli, India, 2019: pp. 788–790. https://doi.org/10.1109/ICOEI.2019.8862582.
  5. F.I. Mowbray, S.M. Fox-Wasylyshyn, M.M. El-Masri, Univariate Outliers: a Conceptual Overview for the Nurse Researcher, Canad. J. Nurs. Res. 51 (2018), 31-37. https://doi.org/10.1177/0844562118786647.
  6. E.O. Merza, N.J. Mohammed, Fast Ways to Detect Outliers, J. Techn. 3 (2021), 66-73. https://doi.org/10.51173/jt.v3i1.287.
  7. A.S. Yaro, F. Maly, P. Prazak, Outlier Detection in Time-series Receive Signal Strength Observation Using Z-score Method with Sn Scale Estimator for Indoor Localization, Appl. Sci. 13 (2023), 3900. https://doi.org/10.3390/app13063900.
  8. E.J. Jamshidi, Y. Yusup, J.S. Kayode, M.A. Kamaruddin, Detecting Outliers in a Univariate Time Series Dataset Using Unsupervised Combined Statistical Methods: a Case Study on Surface Water Temperature, Ecol. Inform. 69 (2022), 101672. https://doi.org/10.1016/j.ecoinf.2022.101672.
  9. W. Berendrecht, M. van Vliet, J. Griffioen, Combining Statistical Methods for Detecting Potential Outliers in Groundwater Quality Time Series, Environ. Monitor. Assess. 195 (2022), 85. https://doi.org/10.1007/s10661-022-10661-0.
  10. B. Dastjerdy, A. Saeidi, S. Heidarzadeh, Review of Applicable Outlier Detection Methods to Treat Geomechanical Data, Geotechnics 3 (2023), 375-396. https://doi.org/10.3390/geotechnics3020022.
  11. O.Y. Rodionova, A.L. Pomerantsev, Detection of Outliers in Projection-based Modeling, Anal. Chem. 92 (2019), 2656-2664. https://doi.org/10.1021/acs.analchem.9b04611.
  12. F. Smarandache, Introduction to Neutrosophic Statistics, Sitech & Education Publishing, 2014.
  13. F. Smarandache, Neutrosophic Statistics is an Extension of Interval Statistics, While Plithogenic Statistics is the Most General Form of Statistics, Infinite Study, 2022.
  14. J. Chen, J. Ye, S. Du, Scale Effect and Anisotropy Analyzed for Neutrosophic Numbers of Rock Joint Roughness Coefficient Based on Neutrosophic Statistics, Symmetry 9 (2017), 208. https://doi.org/10.3390/sym9100208.
  15. J. Chen, J. Ye, S. Du, R. Yong, Expressions of Rock Joint Roughness Coefficient Using Neutrosophic Interval Statistical Numbers, Symmetry 9 (2017), 123. https://doi.org/10.3390/sym9070123.
  16. M. Aslam, On Detecting Outliers in Complex Data Using Dixon’s Test Under Neutrosophic Statistics, J. King Saud Univ. - Sci. 32 (2020), 2005-2008. https://doi.org/10.1016/j.jksus.2020.02.003.
  17. T. Sangeetha, G.M. Amalanathan, Outlier Detection in Neutrosophic Sets by Using Rough Entropy Based Weighted Density Method, CAAI Trans. Intell. Technol. 5 (2020), 121-127. https://doi.org/10.1049/trit.2019.0093.
  18. W. Duan, Z. Khan, M. Gulistan, A. Khurshid, Neutrosophic Exponential Distribution: Modeling and Applications for Complex Data Analysis, Complexity 2021 (2021), 5970613. https://doi.org/10.1155/2021/5970613.
  19. Z. Khan, M. Gulistan, N. Kausar, C. Park, Neutrosophic Rayleigh Model with Some Basic Characteristics and Engineering Applications, IEEE Access 9 (2021), 71277-71283. https://doi.org/10.1109/access.2021.3078150.
  20. J.E. Ricardo, A.J.R. Fernández, T.T.C. Martínez, W.A.C. Calle, Analysis of Sustainable Development Indicators through Neutrosophic Correlation Coefficients, Neutrosophic Sets Syst. 52 (2022), 355-362.
  21. A. AlAita, M. Aslam, Analysis of Covariance Under Neutrosophic Statistics, J. Stat. Comput. Simul. 93 (2022), 397-415. https://doi.org/10.1080/00949655.2022.2108423.
  22. L.A. Al-Essa, Z. Khan, F.S. Alduais, Neutrosophic Logistic Model with Applications in Fuzzy Data Modeling, J. Intell. Fuzzy Syst. 46 (2024), 3867-3880. https://doi.org/10.3233/jifs-233357.
  23. M. Çolak, M. Uçurum, M. Çinar, Ü. Atici, Application of Fuzzy Statistical Process Control for a Manufacturing of GG25 Gray Cast Iron Material, Omer Halisdemir Univ. J. Eng. Sci. 7 (2018), 427-437. https://doi.org/10.28948/ngumuh.387316.23.