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Journal of Statistics and Management Systems

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0014·ISSN (Print): 0972-0510

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Monthly Journal: Publishes peer-reviewed aticles on theoretical and applied statistics and management systems, expoloring industrial statistics, actuarial and decision sciences.

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Journal of Statistics and Management Systems
Open Access Research Article

Analysis of Sudoku square designs for imprecise data

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pp. 741–760Vol. 28Issue 4May 2025DOI: 10.47974/JSMS-1373XML
Received:
06 Dec 2023
Published Online:
09 May 2025
Article type:
Research Article
Language:
EN
Article no.:
JSMS-1373
Pages:
741–760

Abstract

The classic Sudoku square design is applied for testing the null hypothesis when all observations in the data are precise and certain. In some cases, it is difficult for researchers to obtain exact observations due to circumstances beyond their control. Therefore, the observations may be imprecise and noted in intervals. We must therefore search for a suitable generalization of Sudoku square designs in uncertain environments. This paper aims to introduce the four various statistical models of the Sudoku square design under neutrosophic statistics, which provides a solution to the problem of imprecise and uncertain data. The test statistic of the proposed design per model is derived and applied for testing treatment effects. Based on the data analysis, and comparative study, it is concluded that the proposed neutrosophic Sudoku square design is informative, efficient, and adequate for use in the presence of uncertainty.

Keywords

Sudoku square designsClassical statisticsNeutrosophic statisticsUncertain data

Subject Classifications

62A86

References

[1] R. A. Fisher, “Statistical methods for research workers, Edinburg, Oliver and Boyd,” ed: Auflage (1925).
[2] M. Hui-Dong and X. Ru-Gen, “Sudoku Square—a New Design in Field,” Acta Agronomica Sinica, vol. 34, pp. 1489-1493 (2008).
[3] J. Subramani and K. Ponnuswamy, “Construction and analysis of Sudoku designs,” Model assisted statistics and applications, vol. 4, pp. 287-301 (2009).
[4] N. Dauran, A. Odeyale, and A. Shehu, “construction and analysis of balanced incomplete sudoku square design,” Fudma Journal of Sciences, vol. 4, pp. 290-299 (2020).
[5] J. Subramani, “Construction and analysis of orthogonal (Graeco) Sudoku square designs,” Model Assisted Statistics and Applications, vol. 8, pp. 239-246 (2013).
[6] A. Danbaba, “Combined Analysis of Sudoku Square Designs with Same Treatments,” International Journal of Mathematical and Computational Sciences, vol. 10, pp. 189-193 (2016).
[7] J. Sarkar and B. K. Sinha, “Sudoku squares as experimental designs,” Resonance, vol. 20, pp. 788-802 (2015).
[8] A. Shehu and A. Danbaba, “Variance components of models of Sudoku square design,” Ann. Comp. Sci. Seri, vol. 14, pp. 106-113 (2018).
[9] P. Kaur and D. Kumar Garg, “Construction of incomplete Sudoku square and partially balanced incomplete block designs,” Communications in Statistics-Theory and Methods, vol. 49, pp. 1462-1474 (2020).
[10] M. K. Hashmi, A. U. R. Virk, A. J. M. Khalaf, and M. R. Farahani, “Computing irregularity measures for Sudoku graph,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 24, pp. 487-498 (2021).
[11] K. Hamid, M. W. Iqbal, M. U. Ashraf, A. A. Gardezi, S. Ahmad, M. Alqahtani, and M. Shafiq, “Intelligent Systems and Photovoltaic Cells Empowered Topologically by Sudoku Networks,” Computers, Materials & Continua, vol. 74 (2023).
[12] J. Maria Jeyaseeli, G. Lau, W. Shiu, and S. Arumugam, “Sudoku number of graphs,” AKCE International Journal of Graphs and Combinatorics, vol. 20, pp. 209-216 (2023).
[13] F. Smarandache, “Neutrosophic logic-a generalization of the intuitionistic fuzzy logic,” Multispace & multistructure. Neutrosophic transdisciplinarity (100 collected papers of science), vol. 4, p. 396 (2010).
[14] F. Smarandache, “Introduction to neutrosophic statistics: Infinite Study,” Romania-Educational Publisher, Columbus, OH, USA (2014).
[15] J. Chen, J. Ye, and S. Du, “Scale effect and anisotropy analyzed for neutrosophic numbers of rock joint roughness coefficient based on neutrosophic statistics,” Symmetry, vol. 9, p. 208 (2017).
[16] J. Chen, J. Ye, S. Du, and R. Yong, “Expressions of rock joint roughness coefficient using neutrosophic interval statistical numbers,” Symmetry, vol. 9, p. 123 (2017).
[17] M. Aslam, “A new sampling plan using neutrosophic process loss consideration,” Symmetry, vol. 10, p. 132 (2018).
[18] M. Aslam, “A new attribute sampling plan using neutrosophic statistical interval method,” Complex & Intelligent Systems, vol. 5, pp. 365-370 (2019).
[19] M. Aslam, “Neutrosophic analysis of variance: application to university students,” Complex & intelligent systems, vol. 5, pp. 403-407 (2019).
[20] A. AlAita and M. Aslam, “Analysis of covariance under neutrosophic statistics,” Journal of Statistical Computation and Simulation, pp. 1-19 (2022).
[21] M. Aslam and M. Albassam, “Presenting post hoc multiple comparison tests under neutrosophic statistics,” Journal of King Saud University-Science, vol. 32, pp. 2728-2732 (2020).
[22] M. Aslam, “Design of a new Z-test for the uncertainty of Covid-19 events under Neutrosophic statistics,” BMC Medical Research Methodology, vol. 22, pp. 1-6 (2022).
[23] M. Aslam and A. H. Al-Marshadi, “A New Test for Ridge Wind Directional Data Under Neutrosophic Statistics,” Frontiers in Energy Research, p. 399 (2022).
[24] R. Alhabib and A. Salama, “The neutrosophic time series-study its models (linear-logarithmic) and test the coefficients significance of its linear model,” Neutrosophic Sets and Systems, vol. 33, pp. 105-115 (2020).
[25] M. Aslam, “Chi-square test under indeterminacy: an application using pulse count data,” BMC Medical Research Methodology, vol. 21, pp. 1-5 (2021).
[26] R. A. K. Sherwani, H. Shakeel, W. B. Awan, M. Faheem, and M. Aslam, “Analysis of COVID-19 data using neutrosophic Kruskal Wallis H test,” BMC Medical Research Methodology, vol. 21, pp. 1-7 (2021).
[27] R. A. K. Sherwani, H. Shakeel, M. Saleem, W. B. Awan, M. Aslam, and M. Farooq, “A new neutrosophic sign test: An application to COVID-19 data,” Plos one, vol. 16, p. e0255671 (2021).
[28] M. Aslam and M. S. Aldosari, “Analyzing alloy melting points data using a new Mann-Whitney test under indeterminacy,” Journal of King Saud University-Science, vol. 32, pp. 2831-2834 (2020).
[29] M. Aslam, “Introducing Kolmogorov–Smirnov tests under uncertainty: an application to radioactive data,” ACS Omega, vol. 5, pp. 914-917 (2019).
[30] M. Aslam, “Design of the Bartlett and Hartley tests for homogeneity of variances under indeterminacy environment,” Journal of Taibah University for Science, vol. 14, pp. 6-10 (2020).
[31] R. Alhabib and A. Salama, “Using moving averages to pave the neutrosophic time series,” Int. J. Neutrosophic Sci, vol. 3 (2020).
[32] H. L. Huang, “New distance measure of single-valued neutrosophic sets and its application,” International Journal of Intelligent Systems, vol. 31, pp. 1021-1032 (2016).
[33] R. Chutia, M. K. Gogoi, M. A. Firozja, and F. Smarandache, “Ordering single-valued neutrosophic numbers based on flexibility parameters and its reasonable properties,” International Journal of Intelligent Systems, vol. 36, pp. 1831-1850 (2021).
[34] T. Garai and H. Garg, “Possibilistic multiattribute decision making for water resource management problem under single-valued bipolar neutrosophic environment,” International Journal of Intelligent Systems (2021).
[35] D. Pamucar, M. Yazdani, R. Obradovic, A. Kumar, and M. Torres-Jiménez, “A novel fuzzy hybrid neutrosophic decision-making approach for the resilient supplier selection problem,” International Journal of Intelligent Systems, vol. 35, pp. 1934-1986 (2020).
[36] I. Sumathi and C. Antony Crispin Sweety, “New approach on differential equation via trapezoidal neutrosophic number,” Complex & Intelligent Systems, vol. 5, pp. 417-424 (2019).
[37] D. Nagarajan, S. Broumi, F. Smarandache, and J. Kavikumar, “Analysis of neutrosophic multiple regression,” Neutrosophic Sets and Systems, vol. 43, pp. 44-53 (2021).
[38] M. Aslam, “On detecting outliers in complex data using Dixon’s test under neutrosophic statistics,” Journal of King Saud University-Science, vol. 32, pp. 2005-2008 (2020).
[39] M. Aslam, “Introducing Grubbs’s test for detecting outliers under neutrosophic statistics–An application to medical data,” Journal of King Saud University-Science, vol. 32, pp. 2696-2700 (2020).
[40] R. Alhabib, M. M. Ranna, H. Farah, and A. Salama, “Some neutrosophic probability distributions,” Neutrosophic Sets and Systems, vol. 22, pp. 30-38 (2018).
[41] M. Jdid, R. Alhabib, and A. Salama, “Fundamentals of Neutrosophical Simulation for Generating Random Numbers Associated with Uniform Probability Distribution,” Neutrosophic Sets and Systems, vol. 49, p. 6 (2022).
[42] A. AlAita, H. Talebi, M. Aslam, and K. Al Sultan, “Neutrosophic statistical analysis of split-plot designs,” Soft Computing, vol. 27, pp. 7801-7811 (2023).
[43] A. AlAita and H. Talebi, “Exact neutrosophic analysis of missing value in augmented randomized complete block design,” Complex & Intelligent Systems, vol. 10, pp. 509-523 (2024).
[44] S. Ullah, M. Kashif, M. Aslam, G. Haider, A. AlAita, and M. Saleem, “A generalized approach to compute neutrosophic k-factor analysis of variance,” Journal of Intelligent & Fuzzy Systems, pp. 1-13 (2023).
[45] A. AlAita and H. Talebi, “Augmented Latin Square Designs for Imprecise Data,” Neutrosophic Sets and Systems, vol. 57, p. 7 (2023).

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