Fuzzy time series for real-time flood forecasting

  • Chang-Shian Chen
  • You-Da Jhong
  • Wan-Zhen Wu
  • Shien-Tsung ChenEmail author
Original Paper


This study applied fuzzy time series (FTS) analysis to develop a real-time flood forecasting model to forecast typhoon flood discharges. Two crucial factors that influence the performance of FTS are the partition of intervals of the variable and the defuzzification method. This study examined the effects of various interval lengths and two defuzzification methods, the centroid and the midpoint methods, on the model performance. Criteria of model completeness and consistency principle were used to determine the effective interval length, and analytic results showed that the midpoint method outperforms the centroid method. Two structures of forecasting models were proposed to make multiple-hour-ahead flood forecasts. Validation results from typhoon flood events in the Wu River in Taiwan showed that the proposed FTS model, which is novel in hydrologic forecasting, can effectively forecast flood discharges.


Fuzzy time series Flood forecasting Defuzzification Interval length 



  1. Aksoy H, Dahamsheh A (2009) Artificial neural network models for forecasting monthly precipitation in Jordan. Stoch Environ Res Risk A 23(7):917–931. CrossRefGoogle Scholar
  2. Alvisi S, Mascellani G, Franchini M, Bardossy A (2006) Water level forecasting through fuzzy logic and artificial neural network approaches. Hydrol Earth Syst Sci 10(1):1–17. CrossRefGoogle Scholar
  3. Babovic V, Keijzer M (2002) Rainfall runoff modelling based on genetic programming. Nord Hydrol 33(5):1–346CrossRefGoogle Scholar
  4. Bray M, Han D (2004) Identification of support vector machines for runoff modeling. J Hydroinf 6(4):265–280CrossRefGoogle Scholar
  5. Campolo M, Andreussi P, Soldati A (1999) River flood forecasting with a neural network model. Water Resour Res 35(4):1191–1197. CrossRefGoogle Scholar
  6. Chang FJ, Chen YC (2001) A counterpropagation fuzzy-neural network modeling approach to real time streamflow prediction. J Hydrol 245:153–164. CrossRefGoogle Scholar
  7. Chang FJ, Chen YC, Liang JM (2002) Fuzzy clustering neural network as flood forecasting model. Nord Hydrol 33(4):275–290CrossRefGoogle Scholar
  8. Chang FJ, Chiang YM, Chang LC (2007) Multi-step-ahead neural networks for flood forecasting. Hydrol Sci J 52(1):114–130. CrossRefGoogle Scholar
  9. Chen SM (1996) Forecasting enrollments based on fuzzy time series. Fuzzy Sets Syst 81:311–319. CrossRefGoogle Scholar
  10. Chen SM (2002) Forecasting enrollments based on high-order fuzzy time series. Cybern Syst 33:1–16. CrossRefGoogle Scholar
  11. Chen ST (2013) Multiclass support vector classification to estimate typhoon rainfall distribution. Disaster Adv 6(10):110–121Google Scholar
  12. Chen YH, Chang FJ (2009) Evolutionary artificial neural networks for hydrological systems forecasting. J Hydrol 367:125–137. CrossRefGoogle Scholar
  13. Chen MY, Chen BT (2014) Online fuzzy time series analysis based on entropy discretization and a Fast Fourier Transform. Appl Soft Comput 14:156–166. CrossRefGoogle Scholar
  14. Chen SM, Chung NY (2006) Forecasting enrollments using high-order fuzzy time series and genetic algorithms. Int J Intell Syst 21:485–501. CrossRefGoogle Scholar
  15. Chen ST, Yu PS (2007a) Real-time probabilistic forecasting of flood stages. J Hydrol 340:63–77. CrossRefGoogle Scholar
  16. Chen ST, Yu PS (2007b) Pruning of support vector networks on flood forecasting. J Hydrol 347:67–78. CrossRefGoogle Scholar
  17. Chen SH, Lin YH, Chang LC, Chang FJ (2006) The strategy of building a flood forecast model by neuro-fuzzy network. Hydrol Process 20(7):1525–1540. CrossRefGoogle Scholar
  18. Chen TL, Cheng CH, Teoh HJ (2007) Fuzzy time-series based on Fibonacci sequence for stock price forecasting. Phys A 380:377–390. CrossRefGoogle Scholar
  19. Chen TL, Cheng CH, Teoh HJ (2008) High-order fuzzy time-series based on multi-period adaptation model for forecasting stock markets. Phys A 387:876–888. CrossRefGoogle Scholar
  20. Chen ST, Yu PS, Liu BW (2011) Comparison of neural network architectures and inputs for radar rainfall adjustment for typhoon events. J Hydrol 405:150–160. CrossRefGoogle Scholar
  21. Chen PA, Chang LC, Chang FJ (2013a) Reinforced recurrent neural networks for multi-step-ahead flood forecasts. J Hydrol 497:71–79. CrossRefGoogle Scholar
  22. Chen CS, Jhong YD, Wu TY, Chen ST (2013b) Typhoon event-based evolutionary fuzzy inference model for flood stage forecasting. J Hydrol 490:134–143. CrossRefGoogle Scholar
  23. Cheng CH, Chen TL, Wei LY (2010) A hybrid model based on rough sets theory and genetic algorithms for stock price forecasting. Inf Sci 180:1610–1629. CrossRefGoogle Scholar
  24. Chiang YM, Chang FJ (2009) Integrating hydrometeorological information for rainfall–runoff modelling by artificial neural networks. Hydrol Process 23(11):1650–1659. CrossRefGoogle Scholar
  25. Dawson CW, Wilby R (1998) An artificial neural network approach to rainfall–runoff modelling. Hydrol Sci J 43(1):47–66. CrossRefGoogle Scholar
  26. Deo RC, Tiwari MK, Adamowski JF, Quilty JM (2017) Forecasting effective drought index using a wavelet extreme learning machine (W-ELM) model. Stoch Environ Res Risk A 31(5):1211–1240. CrossRefGoogle Scholar
  27. Domanska D, Wojtylak M (2012) Application of fuzzy time series models for forecasting pollution concentrations. Expert Syst Appl 39(9):7673–7679. CrossRefGoogle Scholar
  28. Egrioglu E, Aladag CH, Yolcu U, Uslu VR, Basaran MA (2009) A new approach based on artificial neural networks for high order multivariate fuzzy time series. Expert Syst Appl 36(7):10589–10594. CrossRefGoogle Scholar
  29. Egrioglu E, Aladag CH, Basaran MA, Yolcu U, Uslu VR (2011) A new approach based on the optimization of the length of intervals in fuzzy time series. J Intell Fuzzy Syst 22:15–19Google Scholar
  30. Hadavandi E, Shavandi H, Ghanbari A (2010) Integration of genetic fuzzy systems and artificial neural networks for stock price forecasting. Knowl Based Syst 23:800–808. CrossRefGoogle Scholar
  31. Han D, Chan L, Zhu N (2007) Flood forecasting using support vector machines. J Hydroinf 9(4):267–276. CrossRefGoogle Scholar
  32. Huang YL, Horng SJ, He M, Fan P, Kao TW, Khan MK, Lai JL, Kuo IH (2011) A hybrid forecasting model for enrollments based on aggregated fuzzy time series and particle swarm optimization. Expert Syst Appl 38:8014–8023. CrossRefGoogle Scholar
  33. Huarng K (2001a) Heuristic models of fuzzy time series for forecasting. Fuzzy Sets Syst 123:369–386. CrossRefGoogle Scholar
  34. Huarng K (2001b) Effective lengths of intervals to improve forecasting in fuzzy time series. Fuzzy Sets Syst 123:387–394. CrossRefGoogle Scholar
  35. Huarng K, Yu HK (2004) A dynamic approach to adjusting lengths of intervals in fuzzy time series forecasting. Intell Data Anal 8(1):3–27CrossRefGoogle Scholar
  36. Huarng K, Yu THK (2006) Ratio-based lengths of intervals to improve fuzzy time series forecasting. IEEE Trans Syst Man Cybern Part B Cybern 36(2):328–340. CrossRefGoogle Scholar
  37. Jacquin AP, Shamseldin AY (2009) Review of the application of fuzzy inference systems in river flow forecasting. J Hydroinf 11(3–4):202–210. CrossRefGoogle Scholar
  38. Kant A, Suman PK, Giri BK, Tiwari MK, Chatterjee C, Nayak PC, Kumar S (2013) Comparison of multi-objective evolutionary neural network, adaptive neuro-fuzzy inference system and bootstrap-based neural network for flood forecasting. Neural Comput Appl 23:S231–S246. CrossRefGoogle Scholar
  39. Khu ST, Liong SY, Babovic V, Madsen H, Muttil N (2001) Genetic programming and its application in real-time runoff forecasting. J Am Water Resour Assoc 37(2):439–451. CrossRefGoogle Scholar
  40. Kuo IH, Horng SJ, Kao TW, Lin TL, Lee CL, Pan Y (2009) An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization. Expert Syst Appl 36:6108–6117. CrossRefGoogle Scholar
  41. Lee HS, Chou MT (2004) Fuzzy forecasting based on fuzzy time series. Int J Comput Math 81:781–789CrossRefGoogle Scholar
  42. Lee MH, Sadaei HJ, Suhartono (2013) Improving TAIEX forecasting using fuzzy time series with Box–Cox power transformation. J Appl Stat 40(11):2407–2422. CrossRefGoogle Scholar
  43. Li ST, Cheng YC (2007) Deterministic fuzzy time series model for forecasting enrollments. Comput Math Appl 53:1904–1920. CrossRefGoogle Scholar
  44. Lin GF, Wu MC (2009) A hybrid neural network model for typhoon-rainfall forecasting. J Hydrol 375:450–458. CrossRefGoogle Scholar
  45. Lin GF, Wu MC (2011) An RBF network with a two-step learning algorithm for developing a reservoir inflow forecasting model. J Hydrol 405:439–450. CrossRefGoogle Scholar
  46. Lin GF, Chen GR, Huang PY, Chou YC (2009) Support vector machine-based models for hourly reservoir inflow forecasting during typhoon-warning periods. J Hydrol 372:17–29. CrossRefGoogle Scholar
  47. Lin GF, Chou YC, Wu MC (2013a) Typhoon flood forecasting using integrated two-stage Support Vector Machine approach. J Hydrol 486:334–342. CrossRefGoogle Scholar
  48. Lin GF, Jhong BC, Chang CC (2013b) Development of an effective data-driven model for hourly typhoon rainfall forecasting. J Hydrol 495:52–63. CrossRefGoogle Scholar
  49. Liong SY, Sivapragasam C (2002) Flood stage forecasting with support vector machines. J Am Water Resour Assoc 38(1):173–186. CrossRefGoogle Scholar
  50. Liong SY, Gautam TR, Khu ST, Babovic V, Keijzer M, Muttil N (2002) Genetic programming: a new paradigm in rainfall runoff modeling. J Am Water Resour Assoc 38(3):705–718. CrossRefGoogle Scholar
  51. Lohani AK, Kumar R, Singh RD (2012) Hydrological time series modeling: a comparison between adaptive neuro-fuzzy, neural network and autoregressive techniques. J Hydrol 442:23–35. CrossRefGoogle Scholar
  52. Lohani AK, Goel NK, Bhatia KKS (2014) Improving real time flood forecasting using fuzzy inference system. J Hydrol 509:25–41. CrossRefGoogle Scholar
  53. Lu CC, Chen CH, Yeh TCJ, Wu CM, Yau IF (2006) Integration of transfer function model and back propagation neural network for forecasting storm sewer flow in Taipei metropolis. Stoch Environ Res Risk A 20(1–2):6–22. CrossRefGoogle Scholar
  54. Moeeni H, Bonakdari H (2017) Forecasting monthly inflow with extreme seasonal variation using the hybrid SARIMA-ANN model. Stoch Environ Res Risk A 31(8):1997–2010. CrossRefGoogle Scholar
  55. Mukerji A, Chatterjee C, Raghuwanshi NS (2009) Flood forecasting using ANN, neuro-fuzzy, and neuro-GA models. J Hydrol Eng 14(6):647–652. CrossRefGoogle Scholar
  56. Nayak PC, Sudheer KP, Rangan DM, Ramasastri KS (2004) A neuro-fuzzy computing technique for modeling hydrological time series. J Hydrol 291(1–2):52–66. CrossRefGoogle Scholar
  57. Nayak PC, Sudheer KP, Rangan DP, Ramasastri KS (2005) Short-term flood forecasting with a neurofuzzy model. Water Resour Res 41(4):W04004. CrossRefGoogle Scholar
  58. Nayak PC, Sudheer KP, Jain SK (2007) Rainfall–runoff modeling through hybrid intelligent system. Water Resour Res 43(7):W07415. CrossRefGoogle Scholar
  59. Nguyen PKT, Chua LHC (2012) The data-driven approach as an operational real-time flood forecasting model. Hydrol Process 26(19):2878–2893. CrossRefGoogle Scholar
  60. Rodriguez-Vazquez K, Arganis-Juarez ML, Cruickshank-Villanueva C, Dominguez-Mora R (2012) Rainfall–runoff modelling using genetic programming. J Hydroinf 14(1):108–121. CrossRefGoogle Scholar
  61. See L, Openshaw S (1999) Applying soft computing approaches to river level forecasting. Hydrol Sci J 44(5):763–778. CrossRefGoogle Scholar
  62. Singh SR (2007) A simple method of forecasting based on fuzzy time series. Appl Math Comput 186:330–339. CrossRefGoogle Scholar
  63. Sivapragasam C, Liong SY (2005) Flow categorization model for improving forecasting. Nord Hydrol 36(1):37–48CrossRefGoogle Scholar
  64. Sivapragasam C, Maheswaran R, Venkatesh V (2008) Genetic programming approach for flood routing in natural channels. Hydrol Process 22(5):623–628. CrossRefGoogle Scholar
  65. Song Q, Chissom BS (1993a) Forecasting enrollments with fuzzy time series—Part I. Fuzzy Sets Syst 54:1–9. CrossRefGoogle Scholar
  66. Song Q, Chissom BS (1993b) Fuzzy time series and its models. Fuzzy Sets Syst 54:269–277. CrossRefGoogle Scholar
  67. Song Q, Chissom BS (1994) Forecasting enrollments with fuzzy time series—Part II. Fuzzy Sets Syst 62:1–8. CrossRefGoogle Scholar
  68. Teoh H, Cheng C, Chu H, Chen J (2008) Fuzzy time series model based on probabilistic approach and rough set rule induction for empirical research in stock markets. Data Knowl Eng 67:103–117. CrossRefGoogle Scholar
  69. Toth E, Brath A, Montanari A (2000) Comparison of short-term rainfall prediction models for real-time flood forecasting. J Hydrol 239:132–147. CrossRefGoogle Scholar
  70. Wolfs V, Willems P (2013) A data driven approach using Takagi–Sugeno models for computationally efficient lumped floodplain modeling. J Hydrol 503:222–232. CrossRefGoogle Scholar
  71. Wu MC, Lin GF, Lin HY (2014) Improving the forecasts of extreme streamflow by support vector regression with the data extracted by self-organizing map. Hydrol Process 28(2):386–397. CrossRefGoogle Scholar
  72. Yadav VK, Krishnan M, Biradar RS, Kumar NR, Bharti VS (2013) A comparative study of neural-network and fuzzy time series forecasting techniques—case study: marine fish production forecasting. Indian J Geo-marine Sci 42(6):707–716Google Scholar
  73. Yarar A (2014) A hybrid wavelet and neuro-fuzzy model for forecasting the monthly streamflow data. Water Resour Manag 28(2):553–565. CrossRefGoogle Scholar
  74. Yin Z, Feng Q, Wen X, Deo RC, Yang L, Si J, He Z (2018) Design and evaluation of SVR, MARS and M5Tree models for 1, 2 and 3-day lead time forecasting of river flow data in a semiarid mountainous catchment. Stoch Environ Res Risk A 32(9):2457–2476. CrossRefGoogle Scholar
  75. Yolcu U, Egrioglu E, Uslu VR, Basaran MA, Aladag CH (2009) A new approach for determining the length of intervals for fuzzy time series. Appl Soft Comput 9:647–651. CrossRefGoogle Scholar
  76. Yolcu U, Aladag CH, Egrioglu E (2013) Time-series forecasting with a novel fuzzy time-series approach: an example for Istanbul stock market. J Stat Comput Simul 83(4):599–612. CrossRefGoogle Scholar
  77. Yu PS, Chen ST (2005) Updating real-time flood forecasting using a fuzzy rule-based model. Hydrol Sci J 50(2):265–278CrossRefGoogle Scholar
  78. Yu PS, Chen ST, Chang IF (2006) Support vector regression for real-time flood stage forecasting. J Hydrol 328:704–716. CrossRefGoogle Scholar
  79. Zhang H, Liu D (2006) Fuzzy modeling and fuzzy control. Birkhäuser, New YorkGoogle Scholar
  80. Zhang Z, Zhang Q, Singh VP, Shi P (2018) River flow modelling: comparison of performance and evaluation of uncertainty using data-driven models and conceptual hydrological model. Stoch Environ Res Risk A 32(9):2667–2682. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Chang-Shian Chen
    • 1
  • You-Da Jhong
    • 2
  • Wan-Zhen Wu
    • 2
  • Shien-Tsung Chen
    • 1
    Email author
  1. 1.Department of Water Resources Engineering and ConservationFeng Chia UniversityTaichungTaiwan
  2. 2.Construction and Disaster Prevention Research CenterFeng Chia UniversityTaichungTaiwan

Personalised recommendations