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Fuzzy time series is widely used in forecasting time series data in linguistic forms. Implementing the intuitionistic fuzzy sets (IFS) in fuzzy time series can better handle uncertainties and vagueness in the time series data. However, the time series data always fluctuate randomly and cause drastic changes. In this study, the 4253HT smoother is integrated with the intuitionistic fuzzy time series forecasting model to improve the forecasting accuracy. The proposed model is implemented in predicting the Malaysian crude palm oil prices. The data are firstly smoothed, and followed with the fuzzification process. Next are the transformation of fuzzy sets into IFS and the de-i-fuzzification via equal distribution of hesitancy. The forecasted data are calculated based on the defuzzified values considering the new membership degrees of the IFS after de-i-fuzzification. The results show that the integrated model produces a better forecasting performance compared to the common intuitionistic fuzzy time series forecasting model. In the future, the integration of the data smoothing should be considered before the forecasting of data using fuzzy time series could be performed.


Crude Palm Oil Prices Fuzzy Time Series Intuitionistic Fuzzy Set Smoothing 4253HT Smoother

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How to Cite
Alam, N. M. F., Ramli, N., Mohamed, A. S. T., & Adnan, N. I. M. (2022). Integration of 4253HT Smoother with Intuitionistic Fuzzy Time Series Forecasting Model. Pakistan Journal of Statistics and Operation Research, 18(4), 929-941.


  1. Abhishekh, Gautam, S. S., & Singh, S. R. (2018). A Score Function-Based Method of Forecasting Using Intuitionistic Fuzzy Time Series. New Mathematics and Natural Computation, 14(1), 91–111.
  2. Alam, N. M. F. H. N. B., & Ramli, N. (2021). Time Series Forecasting Model Based on Intuitionistic Fuzzy Set via Equal Distribution of Hesitancy De-I-Fuzzification. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 29(06), 1015–1029.
  3. Alam, N. M. F. H. N. B., Ramli, N., & Nassir, A. A. (2022). Predicting Malaysian Crude Palm Oil Prices Using Intuitionistic Fuzzy Time Series Forecasting Model. ESTEEM Academic Journal, 18, 61–70.
  4. Ansari, A. Q., Philip, J., Siddiqui, S. A., & Alvi, J. A. (2010). Fuzzification of Intuitionistic Fuzzy Sets. 8(3), 94–95.
  5. Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
  6. Azmi, N. N. K., Adam, M. B., Ali, N., & Mustafa, M. S. (2019). Adaptive adjusted compound smoother in recovering signal from noise. ASM Science Journal, 12(Special Issue 1), 256–264.
  7. Bovik, A., Huang, T., & Munson, D. (1983). A generalization of median filtering using linear combinations of order statistics. IEEE Transactions on Acoustics, Speech, and Signal Processing, 31(6), 1342–1350.
  8. dos Santos, F. J. J., & de Arruda Camargo, H. (2014). Forecasting in fuzzy time series by an extension of simple exponential smoothing. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 8864, 257–268.
  9. Ge, P., Wang, J., Ren, P., Gao, H., & Luo, Y. (2013). A new improved forecasting method integrated fuzzy time series with the exponential smoothing method. International Journal of Environment and Pollution, 51(3–4), 206–221.
  10. Hird, J. N., & McDermid, G. J. (2009). Noise reduction of NDVI time series: An empirical comparison of selected techniques. Remote Sensing of Environment, 113(1), 248–258.
  11. Huarng, K. (2001). Effective lengths of intervals to improve forecasting in fuzzy time series. Fuzzy Sets and Systems, 123(3), 387–394.
  12. Joshi, B. P., & Kumar, S. (2012). Intuitionistic fuzzy sets based method for fuzzy time series forecasting. Cybernetics and Systems, 43(1), 34–47.
  13. Jurio, A., Paternain, D., Bustince, H., Guerra, C., & Beliakov, G. (2010). A construction method of Atanassov’s intuitionistic fuzzy sets for image processing. 2010 IEEE International Conference on Intelligent Systems, IS 2010 - Proceedings, 337–342.
  14. Justo dos Santos, F. J., & De Arruda Camargo, H. (2015). A hybrid forecast model combining fuzzy time series, linear regression and a new smoothing technique. Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology, 89(February 2018).
  15. Kumar, S., & Gangwar, S. S. (2015). A fuzzy time series forecasting method induced by intuitionistic fuzzy sets. International Journal of Modeling, Simulation, and Scientific Computing, 6(4).
  16. Lesmana, E., Anggriani, N., Sukono, Fatimah, & Bon, A. T. (2019). Comparison of double exponential smoothing holt and fuzzy time series methods in forecasting stock prices (case study: PT bank central Asia Tbk). Proceedings of the International Conference on Industrial Engineering and Operations Management, July, 1615–1625.
  17. Pedrycz, W. (1993). Fuzzy Control and Fuzzy Systems (Issue June). Research Studies Press Ltd.
  18. Sargent, J., & Bedford, A. (2010). Improving Australian Football League player performance forecasts using optimized nonlinear smoothing. International Journal of Forecasting, 26(3), 489–497.
  19. Singh, P. (2017). A brief review of modeling approaches based on fuzzy time series. International Journal of Machine Learning and Cybernetics, 8(2), 397–420.
  20. Song, Q., & Chissom, B. S. (1993a). Forecasting enrollments with fuzzy time series - Part I. Fuzzy Sets and Systems, 54(1), 1–9.
  21. Song, Q., & Chissom, B. S. (1993b). Fuzzy Time Series and Its Models. Fuzzy Sets and Systems, 54, 269–277.
  22. Song, Q., & Chissom, B. S. (1994). Forecasting enrollments with fuzzy time series - Part II. Fuzzy Sets and Systems, 62(1), 1–8.
  23. Tukey, J. W. (1977). Exploratory Data Analysis. Addison-Wesley Publishing Company Reading.
  24. Velleman, P. F., & Hoaglin, D. C. (1981). Applications, Basics, and Computing of Exploratory Data Analysis. Duxbury Press.
  25. Voskoglou, M. (2019). Application of Fuzzy Numbers to Assessment Processes. In K.-P. Mehdi (Ed.), Encyclopedia of Information Science and Technology (pp. 407–420). IGI Global.
  26. Ye, F., Zhang, L., Zhang, D., Fujita, H., & Gong, Z. (2016). A novel forecasting method based on multi-order fuzzy time series and technical analysis. Information Sciences, 367–368, 41–57.
  27. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.