Nguyen Duy Hieu, Nguyen Cat Ho, Vu Nhu Lan
Author affiliations


  • Nguyen Duy Hieu Tay Bac University
  • Nguyen Cat Ho Institute of Theoretical and Applied Research, Duy Tan University
  • Vu Nhu Lan Thang Long University




Forecasting model, fuzzy time series, hedge algebras, linguistic time series, linguistic logical relationship


Dealing with the time series forecasting problem attracts much attention from the fuzzy community. Many models and methods have been proposed in the literature since the publication of the study by Song and Chissom in 1993, in which they proposed fuzzy time series together with its fuzzy forecasting model for time series data and the fuzzy formalism to handle their uncertainty. Unfortunately, the proposed method to calculate this fuzzy model was very complex. Then, in 1996, Chen proposed an efficient method to reduce the computational complexity of the mentioned formalism. Hwang et al. in 1998 proposed a new fuzzy time series forecasting model, which deals with the variations of historical data instead of these historical data themselves. Though fuzzy sets are concepts inspired by fuzzy linguistic information, there is no formal bridge to connect the fuzzy sets and the inherent quantitative semantics of linguistic words. This study proposes the so-called linguistic time series, in which words with their own semantics are used instead of fuzzy sets. By this, forecasting linguistic logical relationships can be established based on the time series variations and this is clearly useful for human users. The effect of the proposed model is justified by applying the proposed model to forecast student enrollment historical data.


Metrics Loading ...


Q. Song and B. S. Chissom, “Fuzzy time series and its models,” Fuzzy Sets Syst., vol. 54, pp. 269–277, 1993.

Q. Song and B. S. Chissom, “Forecasting enrollments with fuzzy time series - part 1,” Fuzzy Sets Syst., vol. 54, pp. 1–9, 1993.

Q. Song and B. S. Chissom, “Forecasting enrollments with fuzzy time series - part 2,” Fuzzy Sets Syst., vol. 62, pp. 1–8, 1994.

S. M. Chen, “Forecasting enrollments based on fuzzy time series,” Fuzzy Sets Syst., vol. 81, pp. 311–319, 1996.

J. Sullivan and W. H. Woodall, “A comparison of fuzzy forecasting and Markov modeling,” Fuzzy Sets Syst., vol. 64, pp. 279–293, 1994.

J. R. Hwang, S. M. Chen, and C. H. Lee, “Handling forecasting problems using fuzzy time series,” Fuzzy Sets Syst., vol. 100, pp. 217–228, 1998.

S. M. Chen, “Forecasting enrollments based on high-order fuzzy time series,” Cybern. Syst., vol. 33, no. 1, pp. 1–16, 2002.

S. R. Singh, “A computational method of forecasting based on high-order fuzzy time series,” Expert Syst. Appl., vol. 36, no. 7, pp. 10551–10559, 2009.

K. K. Gupta and S. Kumar, “A novel high-order fuzzy time series forecasting method based on probabilistic fuzzy sets,” Granul. Comput., no. 2016, 2019.

S. S. Gangwar and S. Kumar, “Partitions based computational method for high-order fuzzy time series forecasting,” Expert Syst. Appl., vol. 39, no. 15, pp. 12158–12164, 2012.

N. V. Tinh and N. C. Dieu, “A new hybrid fuzzy time series forecasting model based on combining fuzzy c-means clustering and particle swam optimization,” J. Comput. Sci. Cybern., vol. 35, no. 3, pp. 267–292, 2019.

L. W. Lee, S. M. Chen, Y. H. Leu, and L. H. Wang, “Handling Forecasting Problems Based on Two-Factors High-Order Fuzzy Time Series,” IEEE Trans. Fuzzy Syst., vol. 14, p. 10, 2006.

S. M. Chen and S. W. Chen, “Fuzzy forecasting based on two-factors second-order fuzzy-trend logical relationship groups and the probabilities of trends of fuzzy logical relationships,” IEEE Trans. Cybern., vol. 45, no. 3, pp. 405–417, 2015.

W. Zhang, S. Zhang, S. Zhang, D. Yu, and N. N. Huang, “A multi-factor and high-order stock forecast model based on Type-2 FTS using cuckoo search and self-adaptive harmony search,” Neurocomputing, vol. 240, no. 71301142, pp. 13–24, 2017.

M. Khashei, S. R. Hejazi, and M. Bijari, “A new hybrid artificial neural networks and fuzzy regression model for time series forecasting,” Fuzzy Sets Syst., vol. 159, no. 7, pp. 769–786, 2008.

E. Egrioglu, C. H. Aladag, U. Yolcu, and A. Z. Dalar, “A Hybrid High Order Fuzzy Time Series Forecasting Approach Based on PSO and ANNs Methods,” Am. J. Intell. Syst., vol. 6, no. 1, p. 8, 2016.

S. M. Chen and N. Y. Chung, “Forecasting Enrollments of Students by Using Fuzzy Time Series and Genetic Algorithms,” Inf. Manag. Sci., vol. 17, no. 3, pp. 1–17, 2006.

S. M. Chen and B. D. H. Phuong, “Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors,” Knowledge-Based Syst., vol. 118, pp. 204–216, 2017.

S. M. Chen and N. Y. Chung, “Forecasting Enrollments Using High-Order Fuzzy Time Series and Genetic Algorithms,” Int. J. Intell. Syst., vol. 21, pp. 485–501, 2006.

L. W. Lee, L. H. Wang, and S. M. Chen, “Temperature prediction and TAIFEX forecasting based on fuzzy logical relationships and genetic algorithms,” Expert Syst. Appl., vol. 33, p. 12, 2007.

E. Egrioglu, “A New Time-Invariant Fuzzy Time Series Forecasting Method Based on Genetic Algorithm,” Adv. Fuzzy Syst., vol. 2012, p. 6, 2012.

Q. Cai, D. Zhang, B. Wua, and S. C. H. Leung, “A novel stock forecasting model based on fuzzy time series and genetic algorithm,” Procedia Comput. Sci., pp. 1155-1162, 2013.

C. H. Aladag, U. Yolcu, E. Egrioglu, and E. Bas, “Fuzzy lagged variable selection in fuzzy time series with genetic algorithms,” Appl. Soft Comput. J., vol. 22, pp. 465–473, 2014.

I. H. Kuo, S. J. Horng, T. W. Kao, T. L. Lin, C. L. Lee, and Y. Pan, “An improved method for forecasting enrollments based on fuzzy time series and particle swarm optimization,” Expert Syst. Appl., vol. 36, no. 3 PART 2, pp. 6108–6117, 2009.

C. H. Aladag, U. Yolcu, E. Egrioglu, and A. Z. Dalar, “A new time invariant fuzzy time series forecasting method based on particle swarm optimization,” Appl. Soft Comput. J., vol. 12, no. 10, pp. 3291–3299, 2012.

P. Singh and B. Borah, “Forecasting stock index price based on M-factors fuzzy time series and particle swarm optimization,” Int. J. Approx. Reason., vol. 55, no. 3, pp. 812–833, 2014.

C. H. Cheng, G. W. Cheng, and J. W. Wang, “Multi-attribute fuzzy time series method based on fuzzy clustering,” Expert Syst. Appl., vol. 34, p. 8, 2008.

W. Deng, G. Wang, X. Zhang, J. Xu, and G. Li, “A multi-granularity combined prediction model based on fuzzy trend forecasting and particle swarm techniques,” Neurocomputing, vol. 173, pp. 1671–1682, 2016.

H. Wu, H. Long, and J. Jiang, “Handling forecasting problems based on fuzzy time series model and model error learning,” Appl. Soft Comput., vol. 78, pp. 109–118, 2019.

N. C. Ho and W. Wechler, “Hedge Algebras: An algebraic approach to structure of sets of linguistic truth values,” Fuzzy Sets Syst., vol. 35, pp. 281–293, 1990.

H. L. Bui, T. A. Le, and V. B. Bui, “Explicit formula of hedge-algebras-based fuzzy controller and applications in structural vibration control,” Appl. Soft Comput., vol. 60, pp. 150–166, 2017.

H. L. Bui, N. L. Vu, C. H. Nguyen, and C.-H. Nguyen, “General design method of hedge-algebras-based fuzzy controllers and an application for structural active control,” Appl. Intell., vol. 43, p. 25, 2015.

D. T. Tran, V. B. Bui, T. A. Le, and H. Le Bui, “Vibration control of a structure using sliding-mode hedge-algebras-based controller,” Soft Comput., vol. 23, no. 6, pp. 2047–2059, 2017.

C. H. Nguyen, N. L. Vu, and D. A. Nguyen, “Fuzzy controller using hedge algebra based semantics of vague linguistic terms,” in Fuzzy Control Systems, D. Vukadinovic, Ed. Nova Science Publishers, Inc., 2011.

D. Vukadinovic, M. Basic, C. H. Nguyen, N. L. Vu, and T. D. Nguyen, “Hedge-algebra- based voltage controller for a self-excited induction generator,” Control Eng. Pract., vol. 30, p. 13,

N. C. Ho, V. N. Lan, and L. X. Viet, “Optimal hedge-algebras-based controller: Design and application,” Fuzzy Sets Syst., vol. 159, p. 32, 2008.

C. H. Nguyen, T. S. Tran, and D. P. Pham, “Modeling of a semantics core of linguistic terms based on an extension of hedge algebra semantics and its application,” Knowledge-Based Syst., vol. 67, p. 19, 2014.

C. H. Nguyen, V. T. Hoang, and V. L. Nguyen, “A discussion on interpretability of linguistic rule based systems and its application to solve regression problems,” Knowledge-Based Syst., vol. 88, p. 27, 2015.

N. C. Ho and J. M. Alonso, “Looking for a real-world-semantics-based approach to the interpretability of fuzzy systems,” IEEE Int. Conf. Fuzzy Syst., 2017.

N. V. Han and P. C. Vinh, “Modeling with Words Based on Hedge Algebra,” in ICCASA - ICTCC 2018, 2018, no. February.

H. H. Ngo, C. H. Nguyen, and V. Q. Nguyen, “Multichannel image contrast enhancement based on linguistic rule-based intensificators,” Appl. Soft Comput., vol. 76, pp. 744–763, 2019.

N. D. Hieu, V. N. Lan, and N. C. Ho, “Fuzzy time series forecasting based on semantics,” in FAIR Conference, pp. 232–243, 2015. DOI: 10.15625/vap.2015.000156

N. D. Hieu, N. V. Tinh, and V. N. Lan, “A new method to forecast using fuzzy time series based on linguistic semantics,” in FAIR Conference, pp. 435–443, 2016. DOI: 10.15625/vap.2016.00053

N. C. Ho, N. C. Dieu, and V. N. Lan, “The application of hedge algebras in fuzzy time series forecasting,” J. Sci. Technol., vol. 54, no. 2, pp. 161–177, 2016.

H. Tung, N. D. Thuan, and V. M. Loc, “Method of forecasting time series based on hedge algebras based fuzzy time series,” in FAIR Conference, pp. 610–618, 2016. DOI: 10.15625/vap.2016.00075

L. A. Zadeh, “Fuzzy Sets,” Inf. Control, vol. 8, pp. 338–353, 1965.

N. C. Ho and N. V. Long, “Fuzziness measure on complete hedge algebras and quantifying semantics of terms in linear hedge algebras,” Fuzzy Sets Syst., vol. 158, pp. 452–471, 2007.

R. A. Aliev, B. Fazlollahi, R. R. Aliev, and B. Guirimov, “Linguistic time series forecasting using fuzzy recurrent neural network,” Soft Comput., vol. 12, no. 2, pp. 183–190, 2008.

R. Efendi, Z. Ismail, and M. M. Deris, “A new linguistic out-sample approach of fuzzy time series for daily forecasting of Malaysian electricity load demand,” Appl. Soft Comput., vol. 28, pp. 422–430, 2015.




How to Cite

N. D. Hieu, N. C. Ho, and V. N. Lan, “ENROLLMENT FORECASTING BASED ON LINGUISTIC TIME SERIES”, JCC, vol. 36, no. 2, p. 119–137, May 2020.




Most read articles by the same author(s)

1 2 3 4 5 6 > >>