Nguyen Duy Hieu, Nguyen Cat Ho, Pham Đinh Phong, Vu Nhu Lan, Pham Hoang Hiep
Author affiliations


  • Nguyen Duy Hieu Faculty of Natural Sciences and Technology, Tay Bac University, Son La, Vietnam
  • Nguyen Cat Ho Institute of Theoretical and Applied Research, Duy Tan University, Hanoi, Vietnam
  • Pham Đinh Phong Faculty of Information Technology, University of Transport and Communications, Hanoi, Vietnam
  • Vu Nhu Lan Faculty of Mathematics and Informatics, Thang Long University, Hanoi, Vietnam
  • Pham Hoang Hiep HUS High School For Gifted Students, VNU Hanoi - University of Science, Vietnam



Linguistic Time Series, Linguistic Logical Relationship, Hedge Algebras, Quantitative Words Semantics.


Instead of handling fuzzy sets associated with linguistic (L-) labels based on the developers’ intuition immediately, the study follows the hedge algebras (HA-) approach to the time series forecasting problems, in which the linguistic time series forecasting model was, for the first time, proposed and examined in 2020. It can handle the declared forecasting L-variable word-set directly and, hence, the terminology linguistic time-series (LTS) is used instead of the fuzzy time-series (FTS). Instead of utilizing a limited number of fuzzy sets, this study views the L-variable under consideration as to the numeric forecasting variable's human linguistic counterpart. Hence, its word-domain becomes potentially infinite to positively utilize the HA-approach formalism for increasing the LTS forecasting result exactness. Because the forecasting model proposed in this study can directly handle L-words, the LTS, constructed from the numeric time series and its L-relationship groups, considered human knowledges of the given time-series variation helpful for the human-machine interface. The study shows that the proposed formalism can more easily handle the LTS forecasting models and increase their performance compared to the FTS forecasting models when the words’ number grows.


Metrics Loading ...


Song, Q. & Chissom, B. S. Fuzzy time series and its models. Fuzzy Sets Syst. 54, 269–277 (1993). DOI:

Song, Q. & Chissom, B. S. Forecasting enrollments with fuzzy time series - part 1. Fuzzy Sets Syst. 54, 1–9 (1993). DOI:

Song, Q. & Chissom, B. S. Forecasting enrollments with fuzzy time series - part 2. Fuzzy Sets Syst. 62, 1–8 (1994). DOI:

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

Chen, T.-L., Cheng, C.-H. & Teoh, H. J. Fuzzy time-series based on Fibonacci sequence for stock price forecasting. Physica A 380, 14 (2007). DOI:

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

Aladag, C. H., Yolcu, U. & Egrioglu, E. A high order fuzzy time series forecasting model based on adaptive expectation and artificial neural networks. Math. Comput. Simul. 81, 875–882 (2010). DOI:

Egrioglu, E., Aladag, 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). DOI:

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). DOI:

Chen, S. M. & Chen, C. D. TAIEX forecasting based on fuzzy time series and fuzzy variation groups. IEEE Trans. Fuzzy Syst. 19, 1–12 (2011). DOI:

Singh, P. & Borah, B. Forecasting stock index price based on M-factors fuzzy time series and particle swarm optimization. Int. J. Approx. Reason. 55, 812–833 (2014). DOI:

Chen, S. M. & Phuong, B. D. H. Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors. Knowledge-Based Syst. 118, 204–216 (2017). DOI:

Zhang, W., Zhang, S., Zhang, S., Yu, D. & Huang, N. N. A multi-factor and high-order stock forecast model based on Type-2 FTS using cuckoo search and self-adaptive harmony search. Neurocomputing 240, 13–24 (2017). DOI:

Singh, A., Gautam, S. S. & Singh, S. R. A New Type 2 Fuzzy Time Series Forecasting Model Based on Three-Factors Fuzzy Logical Relationships. Int. J. Uncertainty, Fuzziness Knowledge-Based Syst. (2019) doi:10.1142/s0218488519500120. DOI:

Huarng, K. & Yu, H.-K. A Type 2 fuzzy time series model for stock index forecasting. Phys. A Stat. Mech. its Appl. 353, 445–462 (2005). DOI:

Bisht, K. & Kumar, S. Intuitionistic Fuzzy Set-Based Computational Method for Financial Time Series Forecasting. Fuzzy Inf. Eng. 10, 307–323 (2018). DOI:

Cagcag Yolcu, O., Bas, E., Egrioglu, E. & Yolcu, U. A new intuitionistic fuzzy functions approach based on hesitation margin for time-series prediction. Soft Comput. 2, (2019). DOI:

Chen, L.-S., Chen, M.-Y., Chang, J.-R. & Yu, P.-Y. An Intuitionistic Fuzzy Time Series Model Based on New Data Transformation Method. Int. J. Comput. Intell. Syst. 14, 550–559 (2021). DOI:

Singh, S. & Abhishekh, G. A modified weighted method of time series forecasting in intuitionistic fuzzy environment. OPSEARCH (2020) doi:10.1007/s12597-020-00455-8. DOI:

Bas, E., Yolcu, U. & Egrioglu, E. Intuitionistic fuzzy time series functions approach for time series forecasting. Granul. Comput. (2020) doi:10.1007/s41066-020-00220-8. DOI:

Egrioglu, E., Bas, E. & Yolcu, U. Intuitionistic high-order fuzzy time series forecasting method based on pi-sigma artificial neural networks trained by artificial bee colony. Granul. Comput. (2018). DOI:

Egrioglu, E., Bas, E., Yolcu, U. & Yen, M. Picture fuzzy time series : Defining , modeling and creating a new forecasting method. Eng. Appl. Artif. Intell. 88, 13 (2020). DOI:

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

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

Chen, S. M., Wang, N. Y. & Pan, J. S. Forecasting enrollments using automatic clustering techniques and fuzzy logical relationships. Expert Syst. Appl. 36, 11070–11076 (2009). DOI:

Wang, N. Y. & Chen, S. M. Temperature prediction and TAIFEX forecasting based on automatic clustering techniques and two-factors high-order fuzzy time series. Expert Syst. Appl. 36, 2143–2154 (2009). DOI:

Khashei, M., Reza Hejazi, S., Bijari, M., Hejazi, R. & Bijari, M. A new hybrid artificial neural networks and fuzzy regression model for time series forecasting. Fuzzy Sets Syst. 159, 769–786 (2007). DOI:

Egrioglu, E., Aladag, C. H., Yolcu, U., Uslu, V. R. & Basaran, M. A. A new approach based on artificial neural networks for high order multivariate fuzzy time series. Expert Syst. Appl. 36, 10589–10594 (2009). DOI:

Egrioglu, E., Fildes, R. & Baş, E. Recurrent fuzzy time series functions approaches for forecasting. Granul. Comput. 1–8 (2021) doi:10.1007/s41066-021-00257-3. DOI:

Alpaslan, F., Eğrioğlu, E., Hakan Aladağ, Ç. & Tiring, E. An Statistical Research on Feed Forward Neural Networks for Forecasting Time Series. Am. J. Intell. Syst. 2, 21–25 (2012). DOI:

Singh, P. & Huang, Y.-P. A High-Order Neutrosophic-Neuro-Gradient Descent Algorithm-Based Expert System for Time Series Forecasting. Int. J. Fuzzy Syst. (2019) doi:10.1007/s40815-019-00690-2. DOI:

Cagcag Yolcu, O. & Alpaslan, F. Prediction of TAIEX based on hybrid fuzzy time series model with single optimization process. Appl. Soft Comput. 66, 18–33 (2018). DOI:

Kuremoto, T., Hirata, T., Obayashi, M., Mabu, S. & Kobayashi, K. Training Deep Neural Networks with Reinforcement Learning for Time Series Forecasting. in Time Series Analysis - Data, Methods, and Applications 18 (2019). doi: DOI:

Panigrahi, S. & Behera, H. S. A study on leading machine learning techniques for high order fuzzy time series forecasting. Eng. Appl. Artif. Intell. 87, 103245 (2020). DOI:

Chen, S. M. & Hwang, J. R. Temperature Prediction Using Fuzzy Time Series. IEEE Trans. Syst. Man, Cybern. Part B Cybern. 30, 263–275 (2000). DOI:

Lee, L.-W., Wang, L.-H. & Chen, S.-M. Temperature prediction and TAIFEX forecasting based on fuzzy logical relationships and genetic algorithms. Expert Syst. Appl. 33, 12 (2007). DOI:

Hsu, L.-Y. et al. Temperature prediction and TAIFEX forecasting based on fuzzy relationships and MTPSO techniques. Expert Syst. Appl. 37, 15 (2010). DOI:

Wang, C. H. & Hsu, L. C. Constructing and applying an improved fuzzy time series model: Taking the tourism industry for example. Expert Syst. Appl. 34, 2732–2738 (2008). DOI:

Huarng, K.-H., Yu, T. H.-K., Moutinho, L. & Wang, Y.-C. Forecasting tourism demand by fuzzy time series models. Int. J. Cult. Tour. Hosp. Res. 6, 12 (2012). DOI:

Tsaur, R. C. & Kuo, T. C. The adaptive fuzzy time series model with an application to Taiwan’s tourism demand. Expert Syst. Appl. 38, 9164–9171 (2011). DOI:

Yu, H. K. Weighted fuzzy time series models for TAIEX forecasting. Phys. A Stat. Mech. its Appl. 349, 609–624 (2005). DOI:

Qiu, W., Liu, X. & Li, H. A generalized method for forecasting based on fuzzy time series. Expert Syst. Appl. 38, 10446–10453 (2011). DOI:

Duru, O. A fuzzy integrated logical forecasting model for dry bulk shipping index forecasting: An improved fuzzy time series approach. Expert Syst. Appl. 37, 5372–5380 (2010). DOI:

Lee, M. H., Efendi, R. & Ismail, Z. Modified Weighted for Enrollment Forecasting Based on Fuzzy Time Series. MATEMATIKA 25, 12 (2009).

Cheng, C.-H., Teoh, H. J., Chiang, C.-H. & Chen, T.-L. Fuzzy time-series based on adaptive expectation model for TAIEX forecasting. Expert Syst. Appl. 34, 8 (2008). DOI:

Efendi, R., Ismail, Z., Sarmin, N. H. & Mat Deris, M. A reversal model of fuzzy time series in regional load forecasting. Int. J. Energy Stat. 03, 1550003 (2015). DOI:

Rubio, A., Bermúdez, J. D. & Vercher, E. Forecasting portfolio returns using weighted fuzzy time series methods. Int. J. Approx. Reason. 75, 1–12 (2016). DOI:

Ortiz-Arroyo, D. & Poulsen, J. R. A Weighted Fuzzy Time Series Forecasting Model. Indian J. Sci. Technol. 11, 1–11 (2018). DOI:

Ho, N. C. & Wechler, W. Hedge Algebras: An algebraic approach to structure of sets of linguistic truth values. Fuzzy Sets Syst. 35, 281–293 (1990). DOI:

Ho, N. C. & Wechler, W. Extended hedge algebras and their application to fuzzy logic. Fuzzy Sets Syst. 52, 259–281 (1992). DOI:

Ho, N. C., Lan, V. N. & Viet, L. X. Optimal hedge-algebras-based controller: Design and application. Fuzzy Sets Syst. 159, 32 (2008). DOI:

Bui, H. Le, Le, T. A. & Bui, V. B. Explicit formula of hedge-algebras-based fuzzy controller and applications in structural vibration control. Appl. Soft Comput. 60, 150–166 (2017). DOI:

Tran, D. T., Bui, V. B., Le, T. A. & Bui, H. Le. Vibration control of a structure using sliding-mode hedge-algebras-based controller. Soft Comput. 23, 2047–2059 (2017). DOI:

Vukadinovic, D., Basic, M., Nguyen, C. H., Vu, N. L. & Nguyen, T. D. Hedge-algebra-based voltage controller for a self-excited induction generator. Control Eng. Pract. 30, 78–90 (2014). DOI:

Nguyen, C. H., Tran, T. S. & Pham, D. P. Modeling of a semantics core of linguistic terms based on an extension of hedge algebra semantics and its application. Knowledge-Based Syst. 67, 19 (2014). DOI:

Nguyen, C. H., Hoang, V. T. & Nguyen, V. L. A discussion on interpretability of linguistic rule based systems and its application to solve regression problems. Knowledge-Based Syst. 88, 107–133 (2015). DOI:

Ngo, H. H., Nguyen, C. H. & Nguyen, V. Q. Multichannel image contrast enhancement based on linguistic rule-based intensificators. Appl. Soft Comput. 76, 744–763 (2019). DOI:

Hieu, N. D., Ho, N. C. & Lan, V. N. Enrollment Forecasting Based on Linguistic Time Series. J. Comput. Sci. Cybern. 36, 119–137 (2020). DOI:

Hieu, N. D., Ho, N. C. & Lan, V. N. An efficient fuzzy time series forecasting model based on quantifying semantics of words. in RIVF International Conference (2020). DOI:

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

Ho, N. C. & Long, N. Van. Fuzziness measure on complete hedge algebras and quantifying semantics of terms in linear hedge algebras. Fuzzy Sets Syst. 158, 452–471 (2007). DOI:

N. C. Ho, P. T. Lan, N. N. Tu, H. C. Ha, N. T. Anh, "The linguistic summarization and the interpretability, scalability of fuzzy representations of multilevel semantic structures of word-domains", Microprocessors and Microsystems, vol. 81, 103641, 2021. DOI:




How to Cite





Most read articles by the same author(s)

1 2 3 4 5 6 > >>