International Journal of Fuzzy Systems

, Volume 21, Issue 3, pp 852–864 | Cite as

A New Fuzzy Time Series Model Based on Cluster Analysis Problem

  • Tai VovanEmail author
  • Nghiep Ledai


This article proposes a new fuzzy time series (NFTS) model that can interpolate historical data to forecast effectively for the future. In this model, after normalizing original data, we establish the automatic algorithm to determine the suitable number of clusters and to find the fuzzy relationships of each element in series to the established clusters. A principle for forecasting is also proposed from these established fuzzy relationships. The convergence of the proposed algorithm is proven by theory and shown by the numerical examples. The calculation of the proposed model can be performed conveniently and efficiently by a complete Matlab procedure. Comparing with many existing models from a lot of well-known data sets with various scales and characteristics, NFTS model has shown prominent advantages.


Algorithm Cluster Forecast Fuzzy time series Interpolate 


  1. 1.
    Abbasov, A., Manedova, M.: Application of fuzzy time series to population forecasting. Vienna Univ. Technol. 12, 545–552 (2003)Google Scholar
  2. 2.
    Abreu, P.H., Silva, D.C., Mendes-Moreira, J., Reis, L.P., Garganta, J.: Using multivariate adaptive regression splines in the construction of simulated soccer team’s behavior models. Int. J. Comput. Intell. Syst. 6(5), 893–910 (2013)Google Scholar
  3. 3.
    Aladag, S., Aladag, C.H., Mentes, T., Egrioglu, E.: A new seasonal fuzzy time series method based on the multiplicative neuron model and sarima. Hacet. J. Math. Stat. 41(3), 337–345 (2012)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Aladag, C.H., Basaran, M.A., Egrioglu, E., Yolcu, U., Uslu, V.R.: Forecasting in high order fuzzy times series by using neural networks to define fuzzy relations. Expert Syst. Appl. 36(3), 4228–4231 (2009)Google Scholar
  5. 5.
    Alpaslan, F., Cagcag, O., Aladag, C., Yolcu, U., Egrioglu, E.: A novel seasonal fuzzy time series method. Hacet. J. Math. Stat. 41(3), 375–385 (2012)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Bindu, G., Rohit, G.: Enhanced accuracy of fuzzy time series model using ordered weighted aggregation. Appl. Soft Comput. 48, 265–280 (2016)Google Scholar
  7. 7.
    Chen, S.M., Kao, P.Y.: TAIEX forecasting based on fuzzy time series, particle swarm optimization techniques and support vector machines. Inf. Sci. 247, 62–71 (2013)MathSciNetGoogle Scholar
  8. 8.
    Chen, J.H., Hung, W.L.: An automatic clustering algorithm for probability density functions. J. Stat. Comput. Simul. 85(15), 3047–3063 (2015)MathSciNetGoogle Scholar
  9. 9.
    Chen, S.M., Hsu, C.: A new method to forecast enrollments using fuzzy time series. Int. J. Appl. Sci. Eng. 2, 3234–3244 (2004)Google Scholar
  10. 10.
    Chen, S.M.: Forecasting enrollments based on fuzzy time series. Fuzzy Sets Syst. 81(3), 311–319 (1996)MathSciNetGoogle Scholar
  11. 11.
    Egrioglu, E., Aladag, C., Yolcu, U., Basaran, M., Uslu, V.: A new hybrid approach based on SARIMA and partial high order bivariate fuzzy time series forecasting model. Expert Syst. Appl. 36(4), 7424–7434 (2009)Google Scholar
  12. 12.
    Egrioglu, E., Aladag, C., Yolcu, U., Uslu, V., Basaran, M.A.: A new approach based on artificial neural networks for high order multivariate fuzzy time series. Expert Syst. Appl. 36(7), 10589–10594 (2009)Google Scholar
  13. 13.
    Egrioglu, E., Uslu, V., Yolcu, U., Basaran, M., Aladag, C.: A new approach based on artificial neural networks for high order bivariate fuzzy time series. Appl. Soft Comput. 36(7), 265–273 (2009)Google Scholar
  14. 14.
    Eren, B., Vedide, R., Erol, E.: A modified genetic algorithm for forecasting fuzzy time series. Appl. Intell. 41(2), 453–463 (2014)Google Scholar
  15. 15.
    Egrioglu, S., Bas, E., Aladag, C.H., Yolcu, U.: Probabilistic fuzzy time series method based on artificial neural network. Am. J. Intell. Syst. 62, 42–47 (2016)Google Scholar
  16. 16.
    Friedman, J.H.: Multivariate adaptive regression splines. Ann. Stat. 19(1), 1–67 (1991)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Ghosh, H., Chowdhury, S., Prajneshu, S.: An improved fuzzy time-series method of forecasting based on L-R fuzzy sets and its application. J. Appl. Stat. 43(6), 1128–1139 (2015)MathSciNetGoogle Scholar
  18. 18.
    Huarng, K.: Heuristic models of fuzzy time series for forecasting. Fuzzy Sets Syst. 123(3), 369–386 (2001)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Huarng, K., Yu, T.H.K.: Ratio-based lengths of intervals to improve fuzzy time series forecasting. IEEE Trans. Syst. Man Cybern. B (Cybernetics) 36(2), 328–340 (2006)Google Scholar
  20. 20.
    Khashei, M., Bijari, M., Hejazi, C.S.R.: An extended fuzzy artificial neural networks model for time series forecasting. Iran. J. Fuzzy Syst. 3, 45–66 (2011)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Lee, H.S., Chou, M.T.: Fuzzy forecasting based on fuzzy time series. Int. J. Comput. Math. 81(7), 781–789 (2004)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Lewis, P.A., Stevens, J.G.: Nonlinear modeling of time series using multivariate adaptive regression splines (mars). J. Am. Stat. Assoc. 86(416), 864–877 (1991)zbMATHGoogle Scholar
  23. 23.
    Ming, C.S.: Forecasting enrollments based on high-order fuzzy time series. Fuzzy Sets Syst. 33(1), 1–16 (2002)zbMATHGoogle Scholar
  24. 24.
    Own, C.M., Yu, P.T.: Forecasting fuzzy time series on a heuristic high-order model. Cybern. Syst. Int. J. 62(1), 1–8 (2005)zbMATHGoogle Scholar
  25. 25.
    Qiang, S., Brad, C.: Forecasting enrollments with fuzzy time series—part II. Fuzzy Sets Syst. 62(1), 1–8 (1994)Google Scholar
  26. 26.
    Richard, J.H., James, C.B.: Recent convergence results for the fuzzy c-means clustering algorithms. J. Classif. 5, 237–247 (1998)MathSciNetGoogle Scholar
  27. 27.
    Singh, S.: A simple method of forecasting based on fuzzy time series. Appl. Math. Comput. 186(1), 330–339 (2007)MathSciNetzbMATHGoogle Scholar
  28. 28.
    Song, Q., Chissom, B.S.: Forecasting enrollments with fuzzy time series—part I. Fuzzy Sets Syst. 54(3), 269–277 (1993)zbMATHGoogle Scholar
  29. 29.
    Spyros, M., Michle, H.: The \(M_3\)—competition: results, conclusions and implications. Int. J. Forecast. 16(4), 451–476 (2000)Google Scholar
  30. 30.
    Tai, V.V.: An improved fuzzy time series forecasting model using variations of data. Fuzzy Optim. Decis. Making (2018).
  31. 31.
    Teoh, H.J., Cheng, C.H., Chu, H.H., Chen, J.S.: Fuzzy time series model based on probabilistic approach and rough set rule induction for empirical research in stock markets. Data Knowl. Eng. 67(1), 103–117 (2008)Google Scholar
  32. 32.
    Wang, F., Chen, B., Lin, C., Zhang, J., Meng, X.: Adaptive neural network finite-time output feedback control of quantized nonlinear systems. IEEE Trans. Cybern. 48(6), 1839–1848 (2018)Google Scholar
  33. 33.
    Yu, H.K., Huarng, K.: A neural network- based fuzzy time series model to improve forecasting. Expert Syst. Appl. 37, 3366–3372 (2010)Google Scholar
  34. 34.
    Yusuf, S.M., Mohammad, A., Hamisu, A.A.: A novel two-factor high order fuzzy time series with applications to temperature and futures exchange forecasting. Niger. J. Technol. 36(4), 1124–1134 (2017)Google Scholar
  35. 35.
    Zhang, G.P.: Time series forecasting using a hybrid arima and neural network model. Neurocomputing 50, 159–175 (2003)zbMATHGoogle Scholar
  36. 36.
    Zhiqiang, Z., Qiong, Z.: Fuzzy time series forecasting based on k-means clustering. Open J. Appl. Sci. 25(1), 100–105 (2012)Google Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Natural ScienceCan Tho UniversityCan ThoVietnam
  2. 2.College of Basis ScienceNam Can Tho UniversityCan ThoVietnam

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