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Markov Weighted Fuzzy Time-Series Model Based on an Optimum Partition Method for Forecasting Air Pollution

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Abstract

Air pollution is one of the main environmental issues faced by most countries around the world. Forecasting air pollution occurrences is an essential topic in air quality research due to the increase in awareness of its association with public health effects, and its development is vital to managing air quality. However, most previous studies have focused on enhancing accuracy, while very few have addressed uncertainty analysis, which may lead to insufficient results. The fuzzy time-series model is a better option in air pollution forecasting. Nevertheless, it has a limitation caused by utilizing a random partitioning of the universe of discourse. This study proposes a novel Markov weighted fuzzy time-series model based on the optimum partition method. Fitting the optimum partition method has been done based on five different partition methods via two stages. The proposed model is first applied for forecasting air pollution using air pollution index (API) data collected from an air monitoring station located in Klang city, Malaysia. The performance of the proposed model is evaluated based on three statistical criteria, which are the mean absolute percentage error, mean squared error and Theil’s U statistic, using the daily API data. For further validation of the model, it is also implemented for benchmark enrolment data from the University of Alabama. According to the analysis results, the proposed model greatly improved the performance of air pollution index and enrolment prediction accuracy, for which it outperformed several state-of-the-art fuzzy time-series models and classic time-series models. Thus, the proposed model could be a better option for air quality forecasting for managing air pollution.

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References

  1. Wang, X., Yang, Z.: Application of fuzzy optimization model based on entropy weight method in atmospheric quality evaluation: a case study of Zhejiang province, China. Sustainability. 11(7), 21–43 (2019)

    Google Scholar 

  2. Alyousifi, Y., Masseran, N., Ibrahim, K.: Modeling the stochastic dependence of air pollution index data. Stoch. Environ. Res. Risk Assess. 32(6), 1603–1611 (2018)

    Google Scholar 

  3. Yan, Y., Li, Y., Sun, M., Wu, Z.: Primary pollutants and air quality analysis for urban air in China: evidence from Shanghai. Sustainability. 11(8), 2319 (2019)

    Google Scholar 

  4. Wang, D., Zhong, Z., Bai, K., He, L.: Spatial and temporal variabilities of PM2. 5 concentrations in China using functional data analysis. Sustainability. 11(6), 1620 (2019)

    Google Scholar 

  5. Box, G., Jenkins, G.M.: Time Series Analysis: Forecasting and Control, 1st edn. Holden-Day, San Francesco (1976)

    MATH  Google Scholar 

  6. Rahman, N.H., Lee, M.H., Latif, M.T.: Artificial neural networks and fuzzy time series forecasting: an application to air quality. Qual. Quant. 49(6), 2633–2647 (2015)

    Google Scholar 

  7. Kumar, U., Jain, V.K.: ARIMA forecasting of ambient air pollutants (O3, NO, NO2 and CO). Stoch. Environ. Res. Risk Assess. 24(5), 751–760 (2010)

    Google Scholar 

  8. Sharma, P., Chandra, A., Kaushik, S.C.: Forecast using box-Jenkins models for the ambient air quality data of Delhi City. Environ. Monit. Assess. 157(1), 105–112 (2009)

    Google Scholar 

  9. Li, F.: Air quality prediction in Yinchuan by using neural networks. International Conference in Swarm Intelligence. Springer, Berlin, Heidelberg, (2010)

  10. Elangasinghe, M.A., Singhal, N., Dirks, K.N., Salmond, J.A.: Development of an ANN-based air pollution forecasting system with explicit knowledge through sensitivity analysis. Atmos. Pollut. Res. 5(4), 696–708 (2014)

    Google Scholar 

  11. Mishra, D., Goyal, P.: Development of artificial intelligence based NO2 forecasting models at Taj Mahal, Agra. Atmos. Pollut. Res. 6(1), 99–106 (2015)

    Google Scholar 

  12. Nebenzal, A., Fishbain, B.: Long-term forecasting of nitrogen dioxide ambient levels in metropolitan areas using the discrete-time Markov model. Environ. Modell. Softw. 107, 175–185 (2018)

    Google Scholar 

  13. Alyousifi, Y., Ibrahim, K., Kang, W., Zin, W.Z.W.: Markov chain modeling for air pollution index based on maximum a posteriori method. Air Qual. Atmos. Health. 12, 1521–1531 (2019)

    Google Scholar 

  14. Bernard, F.: Fuzzy environmental decision-making: applications to air pollution. Atmos. Environ. 37, 1865–1877 (2003)

    Google Scholar 

  15. Heo, J.S., Kim, D.-S.: A new method of ozone forecasting using fuzzy expert and neural network systems. Sci. Total Environ. 325, 221–237 (2004)

    Google Scholar 

  16. Morabito, F.C., Versaci, M.: Fuzzy neural identification and forecasting techniques to process experimental urban air pollution data. Neural Netw. 16, 493–506 (2003)

    Google Scholar 

  17. Cagcag, O., Yolcu, U., Egrioglu, E., Aladag, C.A.: Novel seasonal fuzzy time series method to the forecasting of air pollution data in Ankara. Am. J. Intell. Syst. 3(1), 13–19 (2013)

    Google Scholar 

  18. David, G.S., Rizol, P.M., Nascimento, L.F.: Fuzzy computational models to evaluate the effects of air pollution on children. Revista Paulista de Pediatria. 36(1), 10–16 (2018)

    Google Scholar 

  19. Aripin, A., Suryono, S., Bayu, S.: Web based prediction of pollutant PM10 concentration using Ruey Chyn Tsaur fuzzy time series model. AIP Conf. Proc. 17(46), 20–46 (2016)

    Google Scholar 

  20. Abdullah, L., Ling, C.Y.: Intervals in fuzzy time series model preliminary investigation for composite index forecasting. ARPN J. Syst. Softw. 2(1), 7–11 (2012)

    Google Scholar 

  21. Dincer, N.G., Akkuş, Ö.: A new fuzzy time series model based on robust clustering for forecasting of air pollution. Ecol. Inf. 43, 157–164 (2018)

    Google Scholar 

  22. Mishra, D., Goyal, P.: Neuro-fuzzy approach to forecast NO2 pollutants addressed to air quality dispersion model over Delhi. Aerosol Air Qual. Res. 16(1), 166–174 (2016)

    Google Scholar 

  23. Darmawan, D., Irawan, M., Syafei, A.D.: Data driven analysis using fuzzy time series for air quality management in Surabaya. Sustinere J. Environ. Sustain. 1(2), 57–73 (2017)

    Google Scholar 

  24. Cheng, C.H., Huang, S.F., Teoh, H.J.: Predicting daily ozone concentration maxima using fuzzy time series based on a two-stage linguistic partition method. Comput. Math. Appl. 62(4), 2016–2028 (2011)

    Google Scholar 

  25. Moustris, K.P., Ziomas, I.C., Paliatsos, A.: 3-day-ahead forecasting of regional pollution index for the pollutants NO2, CO, SO2, and O3 using artificial neural networks in Athens. Water Air Soil Pollut. 209, 29–43 (2010)

    Google Scholar 

  26. Khashei, Bijari M.: An artificial neural network (p, d, q) model for time series forecasting. Expert Syst. Appl. 37, 479–489 (2010)

    Google Scholar 

  27. Prybutok, V.R., Mitchell, D.: Comparison of neural network models with ARIMA and regression models for prediction of Houston’s daily maximum ozone concentrations. Eur. J. Oper. Res. 122, 31–40 (2000)

    MATH  Google Scholar 

  28. Karatzas, Papadourakis, Kyriakidis, I.: Understanding and forecasting atmospheric quality parameters with the aid of ANNs. In: Presented at the neural networks, IJCNN. (IEEE World Congress on Computational Intelligence. (2008)

  29. Song, Q., Chissom, B.S.: Forecasting enrollments with fuzzy time series—part I. Fuzzy Sets Syst. 54, 1–10 (1993)

    Google Scholar 

  30. Song, Q., Chissom, B.S.: Forecasting enrollments with fuzzy time series—part II. Fuzzy Sets Syst. 62(1), 1–8 (1994)

    Google Scholar 

  31. Chen, S.M.: Forecasting enrollments based on fuzzy time series. Fuzzy Sets Syst. 81(3), 311–319 (1996)

    MathSciNet  Google Scholar 

  32. Chen, S.M., Chung, N.Y.: Forecasting enrollments using high-order fuzzy time series and genetic algorithms. Int. J. Intell. Syst. 21(5), 485–501 (2006)

    MATH  Google Scholar 

  33. Chen, S.M.: Forecasting enrollments based on high order fuzzy time series. Cybern. Syst. 33, 1–16 (2002)

    MATH  Google Scholar 

  34. Tsaur, R.C.: A fuzzy time series-Markov chain model with an application to forecast the exchange rate between the Taiwan and US dollar. Int. J. Innov. Comput. Inf. Control 8(7), 4931–4942 (2012)

    Google Scholar 

  35. Cheng, C.H., Chen, T.L., Teoh, H.J., Chiang, C.H.: Fuzzy time series based on adaptive expectation model for TAIEX forecasting. Expert Syst. Appl. 34, 1126–1132 (2008)

    Google Scholar 

  36. Chen, T.L., Cheng, C.H., Jong Teoh, H.: Fuzzy time-series based on Fibonacci sequence for stock price forecasting. Phys. A 380, 377–390 (2007)

    Google Scholar 

  37. Chen, S.M., Chu, H.P., Sheu, T.W.: TAIEX forecasting using fuzzy time series and automatically generated weights of multiple factors. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 42(6), 1485–1495 (2012)

    Google Scholar 

  38. Hsu, L.Y., Horng, S.J., Kao, T.W., Chen, Y.H., Run, R.S., Chen, R.J., Lai, J.L., Kuo, L.H.: Temperature prediction and TAIFEX forecasting based on fuzzy relationships and MTPSO techniques. Expert Syst. Appl. 37(4), 2756–2770 (2010)

    Google Scholar 

  39. Ou, S.L.: Forecasting agricultural output with an improved grey forecasting model based on the genetic algorithm. Comput. Electron. Agric. 85, 33–39 (2012)

    Google Scholar 

  40. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    MATH  Google Scholar 

  41. Huarng, K.: Effective lengths of intervals to improve forecasting in fuzzy time series. Fuzzy Sets Syst. 123(3), 387–394 (2001)

    MathSciNet  MATH  Google Scholar 

  42. Huarng, K., Yu, T.H.: Ratio-based lengths of intervals to improve fuzzy time series forecasting. IEEE Trans. Syst. Man Cybern. Part B Cybern. 36, 328–340 (2006)

    Google Scholar 

  43. Eğrioğlu, E., Aladağ, C.H., Yolcu, U., Uslu, V.R., Basaran, M.A.: Finding an optimal interval length in high order fuzzy time series. Expert Syst. Appl. 37, 5052–5055 (2010)

    Google Scholar 

  44. Egrioglu, E., Aladag, C.H., Basaran, M.A., Yolcu, U., Uslu, V.R.: A new approach based on the optimization of the length of intervals in fuzzy time series. J. Intell. Fuzzy Syst. 22(1), 15–19 (2011)

    MATH  Google Scholar 

  45. Talarposhti, F.M., Sadaei, H.J., Enayatifar, R., Guimarães, F.G., Mahmud, M., Eslami, T.: Stock market forecasting by using a hybrid model of exponential fuzzy time series. Int. J. Approx. Reason. 70, 79–98 (2016)

    MathSciNet  MATH  Google Scholar 

  46. Chen, M.Y., Chen, B.T.: A hybrid fuzzy time series model based on granular computing for stock price forecasting. Inf. Sci. 294, 227–241 (2015)

    MathSciNet  Google Scholar 

  47. Cheng, C.H., Yang, J.H.: Fuzzy time-series model based on rough set rule induction for forecasting stock price. Neurocomputing. 302, 33–45 (2018)

    Google Scholar 

  48. Bose, M., Mali, K.: A novel data partitioning and rule selection technique for modeling high-order fuzzy time series. Appl. Soft Comput. 63, 87–96 (2018)

    Google Scholar 

  49. Rahim, N.F., Othman, M., Sokkalingam, R., Abdul Kadir, E.: Type 2 fuzzy inference-based time series model. Symmetry 11(11), 1340 (2019)

    Google Scholar 

  50. Yu, H.K.: Weighted fuzzy time series models for TAIEX forecasting. Phys. A 349(34), 609–624 (2005)

    Google Scholar 

  51. Cheng, C.H., Chen, T.L., Chiang, C.H.: Trend-weighted fuzzy time-series model for TAIEX forecasting. Neural Inf. Process. 42(34), 469–477 (2006)

    Google Scholar 

  52. Efendi, R., Ismail, Z., Deris, M.M.: Improved weight fuzzy time series as used in the exchange rates forecasting of US Dollar to Ringgit Malaysia. Int. J. Comput. Intell. Appl. 12(01), 13–25 (2013)

    Google Scholar 

  53. Sadaei, H.J., Enayatifar, R., Abdullah, A.H., Gani, A.: Short-term load forecasting using a hybrid model with a refined exponentially weighted fuzzy time series and an improved harmony search. Int. J. Electr. Power Energy Syst. 62, 118–129 (2014)

    Google Scholar 

  54. Abhishekh, S., Kumar, S.: A modified weighted fuzzy time series model for forecasting based on two-factors logical relationship. Int. J. Fuzzy Syst. 21(5), 1403–1417 (2019)

    Google Scholar 

  55. Guan, H., Jie, H., Guan, S., Zhao, A.: A novel fuzzy-Markov forecasting model for stock fluctuation time series. Evol. Intell. (2019). https://doi.org/10.1007/s12065-019-00328-0

    Article  Google Scholar 

  56. Jiang, P., Yang, H., Heng, J.: A hybrid forecasting system based on fuzzy time series and multi-objective optimization for wind speed forecasting. Appl. Energy 235, 786–801 (2019)

    Google Scholar 

  57. Koo, J.W., Wong, S.W., Selvachandran, G., Long, H.V.: Prediction of air pollution index in Kuala Lumpur using fuzzy time series and statistical models. Air Qual. Atmos. Health 13, 77–88 (2020)

    Google Scholar 

  58. Yang, H., Zhu, Z., Li, C., Li, R.: A novel combined forecasting system for air pollutants concentration based on fuzzy theory and optimization of aggregation weight. Appl. Soft Comput. 87, 105972 (2019)

    Google Scholar 

  59. Wang, J., Li, H., Lu, H.: Application of a novel early warning system based on fuzzy time series in urban air quality forecasting in China. Appl. Soft Comput. 71, 783–799 (2018)

    Google Scholar 

  60. Kocak, C.: ARMA (p, q) type high order fuzzy time series forecast method based on fuzzy logic relations. Appl. Soft. Comput. 58, 92–103 (2017)

    Google Scholar 

  61. Department of environment: A guide to air pollutant index in Malaysia (API). Department of environment. Ministry of Science, Technology and the Environment, Kuala Lumpur (2000)

    Google Scholar 

  62. Chang, P.: Fuzzy seasonality forecasting. Fuzzy Sets Syst. 90(1), 1–10 (1997)

    MathSciNet  Google Scholar 

  63. Song, Q.: Seasonal forecasting in fuzzy time series. Fuzzy Sets Syst. 107(2), 235–236 (1999)

    MathSciNet  MATH  Google Scholar 

  64. Cheng, C.H., Chang, J.R., Yeh, C.A.: Entropy-based and trapezoid fuzzification-based fuzzy time series approaches for forecasting IT project cost. Technol. Forecast. Soc. Change 73(5), 524–542 (2006)

    Google Scholar 

  65. Zhang, Z., Zhu, Q.: Fuzzy time series forecasting based on K-means clustering. Open J. Appl. Sci. 2, 100–103 (2012)

    Google Scholar 

  66. Li, S.T., Cheng, Y.C., Lin, S.Y.: A FCM-based deterministic forecasting model for fuzzy time series. Comput. Math. Appl. 56, 3052–3063 (2008)

    MathSciNet  MATH  Google Scholar 

  67. Wang, P., Zhang, H., Qin, Z., Zhang, G.: A novel hybrid-Garch model based on ARIMA and SVM for PM2. 5 concentrations forecasting. Atmos Pollut Res. 8(5), 850–860 (2017)

    Google Scholar 

  68. Silva, P.C.L., Lucas P.O., Sadaei H.J., Guimarães F.J.: pyFTS: fuzzy time series for python. (2018). https://doi.org/10.5281/zenodo.597359

  69. Severiano, C.A., Silva, P.C., Sadaei, H.J., Guimarães, F.G.: Very short-term solar forecasting using fuzzy time series. In: 2017 IEEE international conference on fuzzy systems (FUZZ-IEEE), pp. 1–6 (2017)

  70. Silva, P.C.D., Alves, M. A., Alberto, C., Junior, S., Vieira, G. L., Guimaraes, F., Sadaei, H. J.: Probabilistic forecasting with seasonal ensemble fuzzy time-series. In: XIII Brazilian Congress on Computational Intelligence. (2017)

  71. L-stern Group, L. S.: Time series analysis with ARIMA ARCH/GARCH model in R. Elk Asia Pac. J. 1–19 (2010)

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Acknowledgements

Many thanks to Universiti Teknologi PETRONAS for providing financial support and good facilities. In addition, the authors are grateful to the Department of Environment Malaysia for providing the air pollution data. Additionally, the authors are very thankful to the editor and the anonymous reviewers for their constructive suggestions to improve the quality of this paper.

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Authors and Affiliations

  1. Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32160, Seri Iskandar, Malaysia

    Yousif Alyousifi, Mahmod Othman & Rajalingam Sokkalingam

  2. Center for Intelligent Signal and Imaging Research & Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, 32160, Seri Iskandar, Malaysia

    Ibrahima Faye

  3. Instituto Federal do Norte de Minas Gerais, Januaria, Minas Gerais, Brazil

    Petronio C. L. Silva

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  1. Yousif Alyousifi
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  2. Mahmod Othman
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Alyousifi, Y., Othman, M., Faye, I. et al. Markov Weighted Fuzzy Time-Series Model Based on an Optimum Partition Method for Forecasting Air Pollution. Int. J. Fuzzy Syst. 22, 1468–1486 (2020). https://doi.org/10.1007/s40815-020-00841-w

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