VAGUE DATA ANALYSIS USING SEQUENTIAL TEST
Keywords:
sequential test, neutrosophy, classical test, industry, Bernoulli distribution.DOI:
https://doi.org/10.17654/0972361724023Abstract
Objective. The existing sequential test using Bernoulli distribution can only be applied when no uncertainty/indeterminacy is found in testing the hypothesis. This paper introduces neutrosophic Bernoulli distribution and sequential test using the distribution.
Method. The operational procedure of the proposed test will be introduced and applied for testing the hypothesis in the presence of uncertainty.
Results. The advantages of the proposed test will be discussed using manufacturing data. From the comparison and simulation studies, it is found that the proposed test is efficient than the existing test under classical statistics.
Conclusions. The proposed test may be more economic and time-saving as the decision may make on the basis of the first sample. Therefore, the proposed test is efficient, economical and adequate than the existing test.
Received: October 29, 2023
Accepted: December 16, 2023
References
M. Abdel-Basset, A. Atef and F. Smarandache, A hybrid neutrosophic multiple criteria group decision making approach for project selection, Cognitive Systems Research 57 (2019), 216-227.
M. Abdel-Basset, M. Mohamed, M. Elhoseny, F. Chiclana and A. E.-N. H. Zaied, Cosine similarity measures of bipolar neutrosophic set for diagnosis of bipolar disorder diseases, Artificial Intelligence in Medicine 101 (2019), 101735.
M. Abdel-Basset, N. A. Nabeeh, H. A. El-Ghareeb and A. Aboelfetouh, Utilising neutrosophic theory to solve transition difficulties of IoT-based enterprises, Enterprise Information Systems 14 (2020), 1304-1324.
M. Aslam, Introducing Kolmogorov-Smirnov Tests under Uncertainty: An Application to Radioactive Data, ACS Omega, 2019a.
M. Aslam, Neutrosophic analysis of variance: application to university students, Complex and Intelligent Systems 5(4) (2019b), 403-407.
M. Aslam, Design of the Bartlett and Hartley tests for homogeneity of variances under indeterminacy environment, Journal of Taibah University for Science 14(1) (2020), 6-10.
M. Aslam, Radar data analysis in the presence of uncertainty, European Journal of Remote Sensing 54(1) (2021a), 140-144.
M. Aslam, Testing average wind speed using sampling plan for Weibull distribution under indeterminacy, Scientific Reports 11(1) (2021b), 1-9.
S. Bacanli and D. Icen, Sequential probability ratio test of correlation coefficient using fuzzy hypothesis testing, Open Journal of Statistics 3 (2013), 195-199.
J. Bartroff and J. Song, Sequential tests of multiple hypotheses controlling type I and II familywise error rates, J. Statist. Plann. Inference 153 (2014), 100-114.
S. Broumi, M. Talea, A. Bakali, F. Smarandache and K. Ullah, Bipolar neutrosophic minimum spanning tree, Smart Application and Data Analysis for Smart Cities (SADASC’18), 2018. Available at
SSRN: https://ssrn.com/abstract=3127519.
S. Broumi and F. Smarandache, Correlation coefficient of interval neutrosophic set, Applied Mechanics and Materials 436 (2013), 511-517.
B. D. Causey, Exact calculations for sequential tests based on Bernoulli trials, Comm. Statist. Simulation Comput. 14(2) (1985), 491-495.
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 9(10) (2017), 208.
J. Chen, J. Ye, S. Du and R. Yong, Expressions of rock joint roughness coefficient using neutrosophic interval statistical numbers, Symmetry 9(7) (2017), 123.
N. Chukhrova and A. Johannssen, Nonparametric fuzzy hypothesis testing for quantiles applied to clinical characteristics of COVID-19, International Journal of Intelligent Systems 36(6) (2021), 2922-2963.
T. Denoeux, M.-H. Masson and P.-A. Hebert, Nonparametric rank-based statistics and significance tests for fuzzy data, Fuzzy Sets and Systems 153(1) (2005), 1-28.
D. Dubois and H. Prade, Ranking fuzzy numbers in the setting of possibility theory, Inform. Sci. 30(3) (1983), 183-224.
G. Gardonyi and K. Samu, An enhanced evaluation method of sequential probability ratio test, Math. Probl. Eng. Volume 2019, Article ID 4724507. https://doi.org/10.1155/2019/4724507.
P. Grzegorzewski, Statistical inference about the median from vague data, Control Cybernet. 27 (1998), 447-464.
P. Grzegorzewski, k-sample median test for vague data, International Journal of Intelligent Systems 24(5) (2009), 529-539.
P. Grzegorzewski and M. Spiewak, The sign test and the signed-rank test for interval-valued data, International Journal of Intelligent Systems 34(9) (2019), 2122-2150.
D. Icen, S. Bacanli and S. Gunay, Fuzzy approach for group sequential test, Advances in Fuzzy Systems Volume 2014, Article ID 896150. https://doi.org/10.1155/2014/896150.
J. Kacprzyk, E. Szmidt, S. Zadrozny, K. T. Atanassov and M. Krawczak, Advances in fuzzy logic and technology 2017, Proceedings of: EUSFLAT-2017-The 10th Conference of the European Society for Fuzzy Logic and Technology, September 11-15, 2017, Warsaw, Poland IWIFSGN’2017-The Sixteenth International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, September 13-15, 2017, Warsaw, Poland, Springer, Vol. 2, 2017.
C. Kahraman, C. E. Bozdag, D. Ruan and A. F. Ozok, Fuzzy sets approaches to statistical parametric and nonparametric tests, International Journal of Intelligent Systems 19(11) (2004), 1069-1087.
G. K. Kanji, 100 Statistical Tests, Sage Publishing, 2006.
N. A. Nabeeh, F. Smarandache, M. Abdel-Basset, H. A. El-Ghareeb and A. Aboelfetouh, An integrated neutrosophic-TOPSIS approach and its application to personnel selection: a new trend in brain processing and analysis, IEEE Access 7 (2019), 29734-29744.
J. Pan, Y. Li and V. Y. Tan, Asymptotics of sequential composite hypothesis testing under probabilistic constraints, 2021. arXiv preprint arXiv:2106.00896.
A. Parchami, Fuzzy decision in testing hypotheses by fuzzy data: two case studies, Iran. J. Fuzzy Syst. 17(5) (2020), 127-136.
X. Peng and J. Dai, Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function, Neural Computing and Applications 29(10) (2018), 939-954.
C. A. D. B. Pereira, E. Y. Nakano, V. Fossaluza, L. G. Esteves, M. A. Gannon and A. Polpo, Hypothesis tests for Bernoulli experiments: ordering the sample space by Bayes factors and using adaptive significance levels for decisions, Entropy 19(12) (2017), 696.
S. Pramanik, V. E. Johnson and A. Bhattacharya, A modified sequential probability ratio test, J. Math. Psych. 101 (2021), 102505.
M. Shafiq, M. Atif and R. Viertl, Generalized likelihood ratio test and Cox’s F-test based on fuzzy lifetime data, International Journal of Intelligent Systems 32(1) (2017), 3-16.
A. Shahin, Y. Guo, K. Amin and A. A. Sharawi, A novel white blood cells segmentation algorithm based on adaptive neutrosophic similarity score, Health Information Science and Systems 6(1) (2018), 1.
F. Smarandache, Neutrosophy Neutrosophic Probability, Set, and Logic, ProQuest Information and Learning, Ann. Arbor, Michigan, USA, Vol. 105, 1998, pp. 118-123.
F. Smarandache, Introduction to Neutrosophic Statistics, Sitech and Education Publisher, Romania-Educational Publisher, Craiova, Columbus, Ohio, USA, 2014.
S. Taheri and G. Hesamian, A generalization of the Wilcoxon signed-rank test and its applications, Statist. Papers 54(2) (2013), 457-470.
S. M. Taheri and M. Arefi, Testing fuzzy hypotheses based on fuzzy test statistic, Soft Computing 13(6) (2009), 617-625.
S. M. Taheri and G. Hesamian, Non-parametric statistical tests for fuzzy observations: fuzzy test statistic approach, International Journal of Fuzzy Logic and Intelligent Systems 17(3) (2017), 145-153.
R. Talukdar and H. K. Baruah, A two sample sequential t-test with fuzzy observations, Appl. Math. Sci. 4(68) (2010), 3361-3374.
E. A. Thomas, A note on the sequential probability ratio test, Psychometrika 40(1) (1975), 107-111.
H. Torabi and J. Behboodian, Sequential probability ratio test for fuzzy hypotheses testing with vague data, Austrian Journal of Statistics 34(1) (2005), 25-38.
H. Torabi and S. Mirhosseini, Sequential probability ratio tests for fuzzy hypotheses testing, Appl. Math. Sci. 3(33) (2009), 1609-1618.
R. A. Wijsman, Examples of exponentially bounded stopping time of invariant sequential probability ratio tests when the model may be false, Vol. 1: Theory of Statistics, University of California Press, 1972, pp. 109-128.
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