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Introduction to the Grey Systems Theory and Its Application in Mathematical Modeling and Pandemic Prediction of Covid-19

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Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact

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Abstract

Firstly, this chapter is devoted to present the scientific background for the appearance of Grey Systems in the 1980s. Then, the history of astonishing development, along with the main components and fundamental principles of the Grey Systems, is also introduced. Currently, Grey Systems is an emerging research area with strong possibilities to transect across and apply to a wide range of scientific areas, including industry, agriculture, geology, ecology, medicine, education, etc. However, most applications of the Systems are from Chinese-speaking researchers, while the theory itself is still uncommon in Uncertainty Mathematics. Finally, the representative models with high accuracy are put into practice by predicting and handling the outbreak of Covid-19 pandemic. Not only can the Systems predict the total number of positive cases, but it can also be applied in various other medical practices, including telecare and data management. Their performances are also compared with other uncertainty models, including Machine Learning, which has proven that Grey System models have the ability to perform equally well, or even better, especially in the context of limited data.

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References

  1. Akay, D., Atak, M.: Grey prediction with rolling mechanism for electricity demand forecasting of Turkey. Energy 32(9), 1670–75 (2007). https://doi.org/10.1016/j.energy.2006.11.014

    Article  Google Scholar 

  2. Caydas, U., Hascalık, A.: Use of the grey relational analysis to determine optimum laser cutting parameters with multi-performance characteristics. Optics Laser Technol. 40(7), 987–994 (2008). doi: https://doi.org/10.1016/j.optlastec.2008.01.004

  3. Chang K.-C., Yeh M.-F.: Grey relational analysis based approach for data clustering (2015), IEE Proceedings online no. 20041209. doi: https://doi.org/10.1049/ip-vis:20041209

  4. Chang, S.-C., Lai, H.-C., Yu, H.-C.: A Variable P value rolling grey forecasting model for Taiwan semiconductor industry production. Technol. Forecast. Social Change 72(5), 623–40 (2005). https://doi.org/10.1016/j.techfore.2003.09.002

    Article  Google Scholar 

  5. Chen, C.: Application of the novel nonlinear grey Bernoulli model for forecasting unemployment rate. Chaos, Solit. Fractals 37(1), 278–287. doi: https://doi.org/10.1016/j.chaos.2006.08.024

  6. Chen, L., Liu, Z., Ma, N.: Time-delayed polynomial with the fractional order accumulation. Math. Probl. Eng. (2018). https://doi.org/10.1155/2018/3640625

    Article  Google Scholar 

  7. Chen, Y.-K., Tan, X.-R.: Grey relational analysis on serum markers of liver fibrosis. J. Grey Syst. 1, 63 (1995)

    Google Scholar 

  8. China’s State Council Information Office, Fighting COVID-19: China in Action, June 2020

    Google Scholar 

  9. Dang Y.-G., Liu, S.-F., Chen K-.J.: The GM model that x(n) be taken as initial value. Kybernetes 33(2), 247–254 (2004). doi: https://doi.org/10.1108/03684920410514175

  10. Delcea, C., Scarlat, E.: Grey relational analysis between social media engagement and users’ decisions. In: 2015 IEEE International Conference on Grey Systems and Intelligent Services (GSIS), 2015. doi: https://doi.org/10.1109/gsis.2015.7301843

  11. Deng, J.-L.: Introduction to Grey System Theory 1, 1–24 (1989)

    Google Scholar 

  12. Deng, J.-L.: Control problems of grey systems. Syst. Control Lett. 1(5), 288–94 (1982). https://doi.org/10.1016/s0167-6911(82)80025-x

    Article  MathSciNet  MATH  Google Scholar 

  13. Equbal, Md. I., Kumar, R., Shamim, M., Ohdar, R.K.: A grey-based Taguchi method to optimize hot forging process. Procedia Mater. Sci. 6, 1495–1504 (2014). doi: https://doi.org/10.1016/j.mspro.2014.07.129

  14. Guo, R.: A repairable system modelling: combining grey system theory with interval-valued fuzzy set theory. Int. J. Reliab. Qual. Safety Eng. 12(03), 241–66 (2005). https://doi.org/10.1142/s0218539305001811

    Article  Google Scholar 

  15. Hsin, P.-H. Forecasting Taiwan’s GDP by the novel Nash nonlinear Grey Bernoulli model with trembling-hand perfect equilibrium, 2013. doi: https://doi.org/10.1063/1.4823908

  16. Hollander, J.E., Carr, B.G.: Virtually Perfect? Telemedicine for Covid-19. New Engl. J. Med. 382(18), 1679–1681. doi: https://doi.org/10.1056/nejmp2003539

  17. Huang J-.C.: Application of grey system theory in telecare. Comput. Biol. Med. 41(5), 302–306 (2011). doi: https://doi.org/10.1016/j.compbiomed.2011.03.007

  18. Huang, W., Shi, H.-R., Tan, X.-R.: A grey relational study on determination of stroke volume with D and M echocardiography. J. Grey Syst. 3, 203 (1994)

    Google Scholar 

  19. Jin, X.-Z.: Grey correlation cluster method and it’s application study. J. Henan Med. Coll. Staff Workers 11(4), 1–4 (1999)

    Google Scholar 

  20. Juan, L., Liu, W.-J.: Population forecasting in China based on the Grey-Markov model. In: 2011 International Conference on Information Management, Innovation Management and Industrial Engineering, 2011. doi: https://doi.org/10.1109/iciii.2011.315

  21. Kalsi, N.S., Sehgal, R., Sharma, V.S.: Multi-objective optimization using Grey relational Taguchi analysis in machining. Int. J. Organ. Collect. Intell. 6(4), 45–64 (2016). https://doi.org/10.4018/ijoci.2016100103

    Article  Google Scholar 

  22. Keshvardoost, S., Bahaadinbeigy, K., Fatehi, F.: Role of telehealth in the management of COVID-19: lessons learned from previous SARS, MERS, and Ebola outbreaks. Telemedicine and E-Health. doi: https://doi.org/10.1089/tmj.2020.0105

  23. Kose, E., Burmaoglu, S., Kabak, M.: Grey relational analysis between energy consumption and economic growth. Grey Syst.: Theory Appl. 3(3), 291–304 (2013). https://doi.org/10.1108/gs-06-2013-0010

    Article  Google Scholar 

  24. Kuo, Y., Yang, T., Huang, G.-W.: The Use of Grey Relational Analysis in Solving Multiple Attribute Decision-Making Problems. Computers & Industrial Engineering 55(1), 80–93 (2008). https://doi.org/10.1016/j.cie.2007.12.002

    Article  Google Scholar 

  25. Li, G.-D., Yamaguchi, D., Nagai, M.: A GM(1,1)-Markov chain combined model with an application to predict the number of Chinese International Airlines. Technol. Forecast. Soc. Change 74(8), 1465–81 (2007). https://doi.org/10.1016/j.techfore.2006.07.010

    Article  Google Scholar 

  26. Lin B.-Y., Gao, F., Wang, M., et al.: A parameter estimation of fractional order grey model based on adaptive dynamic Cat Swarm Algorithm (2018), arXiv:1805.08680

  27. Liu, L., Wang, Q.-R., Wang, J.-Z., Liu, M.:A Rolling Grey Model optimized by particle swarm optimization in economic prediction. Comput. Intell. 32(3), 391–419. doi: https://doi.org/10.1111/coin.12059

  28. Liu, P.-J., Dong, G.-Y.: Applying grey relational grade in determining pharmacokinetic modeling. J. Chinese Hosp. Pharmacy 3, 141 (1996)

    Google Scholar 

  29. Liu, S., Yi, L.: Grey Information: Theory and Practical Applications. England: Springer, London Ltd, 2010. doi: https://doi.org/10.1016/j.techfore.2006.07.010

  30. Liu, S., Yi, L.: An introduction to grey systems: foundations, methodology and applications. Kybernetes 32(4) (2003). doi: https://doi.org/10.1108/k.2003.06732dae.008

  31. Lu, J.-S., Xie, W.-D., et al.: An optimized nonlinear grey Bernoulli model and its application. Neurocomputing 17, 206–214 (2016). https://doi.org/10.1016/j.neucom.2015.11.032

    Article  Google Scholar 

  32. Ma, X., Xie, M., Wu, W., Zeng, B., Wang, Y., Wu, X.: The novel fractional discrete multivariate Grey system model and its applications. Appl. Math. Modell. 70, 402–24 (2019). https://doi.org/10.1016/j.apm.2019.01.039

    Article  MathSciNet  MATH  Google Scholar 

  33. Mao, S., Gao, M., Xiao, X., Zhu, M.: A novel fractional Grey system model and its application. Appl. Math. Modell. 40(7–8), 5063–76 (2016). https://doi.org/10.1016/j.apm.2015.12.014

    Article  MathSciNet  MATH  Google Scholar 

  34. Ngo, H.-A., Hoang, T.-N.: A Rolling Optimized Nonlinear Grey Bernoulli model and application in predicting total COVID-18 infected cases (2020). Accepted paper at the 2020 International Congress for Grey Systems and Uncertainty Analysis, Nanjing

    Google Scholar 

  35. Nguyen, P.-H., Sheu, T.-W., Nguyen, P.-T., Pham, D.-H., Nagai, M.: Taylor approximation method in grey system theory and its application to predict the number of foreign students studying in Taiwan. Int. J. Innov. Sci. Res. 10(2), 409–420 (2014)

    Google Scholar 

  36. Rausch N., Wright, T.: The role of data management techniques during COVID-19: 4 examples (2020), SAS Blogs

    Google Scholar 

  37. Reducing Ebola Virus Transmission: Improving Contact Tracing in Sierra Leone. (2020, March 19). Retrieved July 06, 2020, from https://www.poverty-action.org/study/reducing-ebola-virus-transmission-improving-contact-tracing-sierra-leone

  38. Sahin, U., Sahin, T.: Forecasting the cumulative number of confirmed cases of COVID-19 in Italy, UK and USA using fractional nonlinear grey Bernoulli model. Chaos, Solit. Fractals 138, 109948 (2020). https://doi.org/10.1016/j.chaos.2020.109948

  39. Shen, X., Ou, L., Tan, X.: Applications of Grey prediction model for quantity prediction of medical supplies: a case study. In: Proceedings of 2013 IEEE International Conference on Grey systems and Intelligent Services (GSIS), 2013. doi: https://doi.org/10.1109/gsis.2013.6714772

  40. Tan, G.-T.: The structure method and application of background value in grey system GM model (I), Syst. Eng.-Theory Pract. 4, 98–103 (2000)

    Google Scholar 

  41. Tan, X.R., Deng, J.L., Pan, H.X., Liu, S.F.: Grey system and Grey data management in medicine. In: Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services. doi: https://doi.org/10.1109/GSIS.2007.4443258

  42. Tan, X.-R., Deng, J.-L., Xu, Y.-C.: The statistical and grey relational analysis of the pressure-lowering effect of captopril. The academic seminar proceedings of the national clinical evaluation of the cardiovascular drugs. The expert committee of clinical drug evaluation of Chinese Medical Association, 1996: 127

    Google Scholar 

  43. Tan, X.-R., Li, Y.-G., Chen, M.-Z.: Applications of gray relational analysis in gastroenterology. World J. Gastroenterol. 11(22): 3457–3460. doi: https://doi.org/10.3748/wjg.v11.i22.3457

  44. Tien, T.-L.: A research on the grey prediction model GM(1, n). Appl. Math. Comput. 218, 4903–4916 (2012). https://doi.org/10.1016/j.amc.2011.10.055

    Article  MathSciNet  MATH  Google Scholar 

  45. What is Telecare? A Definition of Services, Technologies & Equipment. (2020, January 28). Retrieved July 06, 2020, from https://evisit.com/resources/what-is-telecare/

  46. Chia-Nan, W., Van-Thanh, P.: An improved nonlinear Grey Bernoulli model combined with fourier series. Math. Probl. Eng. 2015, 1–7 (2015). https://doi.org/10.1155/2015/740272

    Article  Google Scholar 

  47. Wang, Y., Tang, J., Cao, W.: Grey prediction model-based food security early warning prediction. Proceedings of 2011 IEEE International Conference on Grey Systems and Intelligent Services (2011). doi: https://doi.org/10.1109/gsis.2011.6043997

  48. Wang, Z.-W., Dang, Y.-G., et al.: Solution of GM(1,1) power model and its properties. Syst. Eng. Electrion. 31(10), 2380–2383 (2009)

    MATH  Google Scholar 

  49. Wang, Z.-X.: Nonlinear Grey prediction model with convolution integral NGMC (1, n) and its application to the forecasting of China’s industrial SO\(_{2}\) emissions. J. Appl. Math. 580161 (2014). doi: https://doi.org/10.1155/2014/580161

  50. Wang, Z.-X., Hipel, K.W., Wang, Q., He, S.-W.: An optimized NGBM(1,1) model for forecasting the qualified discharge rate of industrial wastewater in China. Appl. Math. Modell. 35(12), 5524–32 (2011). https://doi.org/10.1016/j.apm.2011.05.022

    Article  Google Scholar 

  51. Wei, L., Dang, Y.-G.: The optimized grey model GM(l, N) based on the development trends of driving variables and its application. In: IEEE International Conference on Systems, Man, and Cybernetic (SMC), Budapest, Hungary (2016). doi: https://doi.org/10.1109/SMC.2016.7844247

  52. Wu, L., Liu, S., Yao, L., Yan, S., Liu, D.: Grey system model with the fractional order accumulation. Commun. Nonlinear Sci. Numer. Simul. 18(7), 1775–85 (2013). https://doi.org/10.1016/j.cnsns.2012.11.017

    Article  MathSciNet  MATH  Google Scholar 

  53. Wu, W.-H., Lin, C.-T., Peng, K.-H., Huang, C.-C.: Applying hierarchical grey relation clustering analysis to geographical information systems – A case study of the hospitals in Taipei City. Expert Syst. Appl. 39, 7247–7254 (2012). https://doi.org/10.1016/j.eswa.2012.01.052

    Article  Google Scholar 

  54. Wu, W.-Z., Zhang, T., Zheng, C.: A novel optimized nonlinear Grey Bernoulli model for forecasting China’s GDP. Complexity 2019, 1–10 (2019). https://doi.org/10.1155/2019/1731262

    Article  Google Scholar 

  55. Yang, S.Q.: Public health statistics. the People’s Health Press, Beijing (1978)

    Google Scholar 

  56. Yang, Y.J., Liu, S.F., Xie, N.M.: Uncertainty and grey data analytics. Marine Econ. Manag. (2019). https://doi.org/10.1108/MAEM-08-2019-0006

    Article  Google Scholar 

  57. Yang, Y.-K.: Optimization of injection-molding process for mechanical and tribological properties of short glass fiber and polytetrafluoroethylene reinforced polycarbonate composites with Grey relational analysis: a case study. Polymer-Plastics Technol. Eng. 45(7), 769–777 (2006). https://doi.org/10.1080/03602550600611826

    Article  Google Scholar 

  58. Yang, Y.Y., Shie, J.R., Huang, C.H.: Optimization of dry machining parameters for high purity graphite in end-milling process. Mater. Manuf. Process. 21, 832–7 (2006). https://doi.org/10.1080/03602550600728141

    Article  Google Scholar 

  59. Zeng, B., Luo, C.: Forecasting the total energy consumption in China using a new-structure Grey system model. Grey Syst.: Theory Appl. 7(2), 194–217 (2017). https://doi.org/10.1108/gs-05-2017-0011

    Article  Google Scholar 

  60. Zeng, B., Duan, H., Zhou, Y.: A new multivariable grey prediction model with structure compatibility. Appl. Math. Modell. doi: https://doi.org/10.1016/j.apm.2019.05.044

  61. Zhao, Y.-F., Shou, M.-H., Wang, Z.-X.: Prediction of the number of patients infected with COVID-19 based on rolling Grey Verhulst models. Int. J. Environ. Res. Public Health 17, 4582 (2020). https://doi.org/10.3390/ijerph17124582

    Article  Google Scholar 

  62. Mao, Z.-L., Sun, J.-H.: Application of Grey-Markov model in forecasting fire accidents. Procedia Eng. 11, 314–18 (2011). https://doi.org/10.1016/j.proeng.2011.04.663

    Article  Google Scholar 

  63. Zhou, W., He, J.-M.: Generalized GM (1, 1) model and its application in forecasting of fuel production. Appl. Math. Modell. 37(9), 6234–43 (2013). https://doi.org/10.1016/j.apm.2013.01.002

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. École Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France

    Hoang Anh Ngo

  2. Department of Mathematics and Computer Science, Beloit College, Beloit, WI, 53511, USA

    Thai Nam Hoang & Mehmet Dik

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  1. Hoang Anh Ngo
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  2. Thai Nam Hoang
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  3. Mehmet Dik
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Correspondence to Mehmet Dik .

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Editors and Affiliations

  1. Anand International College of Engineering, Jaipur, Rajasthan, India

    Praveen Agarwal

  2. Institute of Mathematics, University of Santiago de Compostela, Santiago, Spain

    Juan J. Nieto

  3. Mathematical Sciences, Queen Mary University of London, London, UK

    Michael Ruzhansky

  4. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Delfim F. M. Torres

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Ngo, H.A., Hoang, T.N., Dik, M. (2021). Introduction to the Grey Systems Theory and Its Application in Mathematical Modeling and Pandemic Prediction of Covid-19. In: Agarwal, P., Nieto, J.J., Ruzhansky, M., Torres, D.F.M. (eds) Analysis of Infectious Disease Problems (Covid-19) and Their Global Impact. Infosys Science Foundation Series(). Springer, Singapore. https://doi.org/10.1007/978-981-16-2450-6_10

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