Forecasting model of intuitionistic fuzzy time series using ratio distribution

Nguyen Thi Thu Dung, L.V. Chernenkaya


Time series forecasting modeling is an area of intensive research and development. Nowadays, the application of fuzzy logic to time series forecasting models has attracted much attention and developed widely. At this time, the intuitionistic fuzzy time series model is not only a new approach, but also demonstrates high forecasting performance when nondeterminism is taken into account. In this paper, a modified intuitionistic fuzzy time series forecasting model is proposed based on discretization optimization based on the determination of the optimal ratio using the allocation algorithm. The model is applied to a real time series forecasting problem obtained from historical data at the University of Alabama from 1971 to 1992. The mean square errors (MSE) of the obtained forecasting results are presented. The superiority of the proposed model is demonstrated by comparing it with existing models.

Full Text:

PDF (Russian)


N. T. T. Dung and Chernenkaya L. V., “System analysis in managing the development of territorial complexes in Vietnam,” in the collection: System analysis in design and management, collection of scientific papers of the XXV International Scientific and Educational-Practical Conference, St. Petersburg, 2021, pp. 346–352. (in russian)

N. T. T. Dung and Chernenkaya L. V., “Models for analyzing the economic development of several regions of Vietnam based on mathematical methods of multivariate statistics,” in In: Impulse of Organizational Innovation. Collection of competitive works of the 1st interuniversity competition for students, undergraduates and graduate students, Moscow, 2020, pp. 301–324. (in russian)

L. A. Zadeh, “Fuzzy Sets,” Information and control, vol. 8, pp. 338–353, 1965.

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 I,” Fuzzy Sets Syst, vol. 54, pp. 1–9, 1993.

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

Manish Pant, A. K. Shukla, and Sanjay Kumar, “A novel method to optimize interval length for intuitionistic fuzzy time series,” in Soft Computing for Problem Solving, Advances in Intelligent Systems and Computing, Pantnagar, Uttarakhand, India, 2020, pp. 55–62. [Online]. Available:

J. Montero, D. Gómez, and H. Bustince, “Atanassov’s intuitionistic fuzzy sets as a classification model,” in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Springer Verlag, 2007, pp. 69–75. doi: 10.1007/978-3-540-72950-1_7.

K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets Syst, vol. 20, pp. 87–96, 1986.

N. T. T. Dung and Chernenkaya L. V., “A model of factor analysis based on fuzzy c-means clustering,” in Journal News of Tula State University - Technical Sciences (Tula State University, Tula), Tula: Tula State University Publishing House, 2023, pp. 329–336. (in russian)

B. P. Joshi and S. Kumar, “Intuitionistic fuzzy sets based method for fuzzy time series forecasting,” Cybernetics and Systems, vol. 43, no. 1. pp. 34–47, Jan. 2012. doi: 10.1080/01969722.2012.637014.

S. Kumar and S. S. Gangwar, “Intuitionistic Fuzzy Time Series: An Approach for Handling Nondeterminism in Time Series Forecasting,” IEEE Transactions on Fuzzy Systems, vol. 24, no. 6, pp. 1270–1281, Dec. 2016, doi: 10.1109/TFUZZ.2015.2507582.

A. Jurio, D. Paternain, H. Bustince, C. Guerra, and G. Beliakov, “A construction method of Atanassov’s Intuitionistic fuzzy set for image processing,” in 5th IEEE International Conference Intelligent Systems, Institute of Electrical and Electronics Engineers, Ed., University of Westminster, London, UK: 2020 IEEE International Conference on Intelligent Systems, Jul. 2010, pp. 337–342.

Abhishekh, S. S. Gautam, and S. R. Singh, “A refined method of forecasting based on high-order intuitionistic fuzzy time series data,” Progress in Artificial Intelligence, vol. 7, no. 4, pp. 339–350, Dec. 2018, doi: 10.1007/s13748-018-0152-x.

K. Huarng, “Effective lengths of intervals to improve forecasting in fuzzy time series,” Fuzzy Sets Syst, vol. 123, pp. 387–394, 2001, [Online]. Available:

Abhishekh, S. S. Gautam, and S. R. Singh, “A new method of time series forecasting using intuitionistic fuzzy set based on average-length,” Journal of Industrial and Production Engineering, vol. 37, no. 4, pp. 175–185, May 2020, doi: 10.1080/21681015.2020.1768163.

Abhishekh, S. S. Gautam, and S. R. Singh, “A Score Function-Based Method of Forecasting Using Intuitionistic Fuzzy Time Series,” New Mathematics and Natural Computation, vol. 14, no. 1, pp. 91–111, Mar. 2018, doi: 10.1142/S1793005718500072.

K. Bisht and S. Kumar, “Intuitionistic Fuzzy Set-Based Computational Method for Financial Time Series Forecasting,” Fuzzy Information and Engineering, vol. 10, no. 3, pp. 307–323, Jul. 2018, doi: 10.1080/16168658.2019.1631557.

S. S. Gautam, Abhishekh, and S. R. Singh, “A modified weighted method of time series forecasting in intuitionistic fuzzy environment,” OPSEARCH, vol. 57, no. 3, pp. 1022–1041, Sep. 2020, doi: 10.1007/s12597-020-00455-8.

Farhan Nik Muhammad, Nazirah Ramli, and Asyura Abd Nassir, “Comparison of interval lengths for the intuitionistic fuzzy time series forecasting model,” GADING Journal of Science and Technology, vol. 5, no. 1, pp. 36–43, Mar. 2022, [Online]. Available:

Manish Pant, A. K. Shukla, and Sanjay Kumar, “Novel Intuitionistic fuzzy time series modeling to forecast the death cases of COVID-19 in India,” in Lecture Notes in Networks and Systems, Smart trends in Computing and Communications, Ed., 2021, pp. 525–531. [Online]. Available:

A. Singh, D. K. Joshi, and S. Kumar, “A novel construction method of intuitionistic fuzzy set from fuzzy set and its application in multi-criteria decision-making problem,” in Advances in Intelligent Systems and Computing, Springer Verlag, 2019, pp. 67–75. doi: 10.1007/978-981-13-0680-8_7.

E. Bas, U. Yolcu, and E. Egrioglu, “Intuitionistic fuzzy time series functions approach for time series forecasting,” Granular Computing, vol. 6, no. 3, pp. 619–629, Jul. 2021, doi: 10.1007/s41066-020-00220-8.

O. Cagcag Yolcu and U. Yolcu, “A novel intuitionistic fuzzy time series prediction model with cascaded structure for financial time series,” Expert Syst Appl, vol. 215, Apr. 2023, doi: 10.1016/j.eswa.2022.119336.

Z. Xu and R. R. Yager, “Some geometric aggregation operators based on intuitionistic fuzzy sets,” Int J Gen Syst, vol. 35, no. 4, pp. 417–433, Aug. 2006, doi: 10.1080/03081070600574353.

Z. Xu, “Intuitionistic fuzzy aggregation operators,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 6, pp. 1179–1187, Dec. 2007, doi: 10.1109/TFUZZ.2006.890678.

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

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

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, no. 2, pp. 1235–1242, Feb. 2008, doi: 10.1016/j.eswa.2006.12.013.

C. H. Cheng, T. L. Chen, H. J. Teoh, and C. H. Chiang, “Fuzzy time-series based on adaptive expectation model for TAIEX forecasting,” Expert Syst Appl, vol. 34, no. 2, pp. 1126–1132, Feb. 2008, doi: 10.1016/j.eswa.2006.12.021.

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

Jilani Tahseen Ahmed, S. M. Aquil Burney, and C. Ardil, “Multivariate High Order Fuzzy Time Series Forecasting for Car Road Accidents,” International Scholarly and Scientific Research & Innovation, vol. 2, no. 6, pp. 2038–2043, 2007, [Online]. Available:

W. Qiu, X. Liu, and H. Li, “A generalized method for forecasting based on fuzzy time series,” Expert Syst Appl, vol. 38, no. 8, pp. 10446–10453, Aug. 2011, doi: 10.1016/j.eswa.2011.02.096.

K. Huarng, “Heuristic models of fuzzy time series for forecasting,” Fuzzy Sets Syst, vol. 123, pp. 369–386, 2001, [Online]. Available:

R. C. Tsaur, J. C. O Yang, and H. F. Wang, “Fuzzy relation analysis in fuzzy time series model,” Computers and Mathematics with Applications, vol. 49, no. 4, pp. 539–548, Feb. 2005, doi: 10.1016/j.camwa.2004.07.014.

S. R. Singh, “A simple method of forecasting based on fuzzy time series,” Appl Math Comput, vol. 186, no. 1, pp. 330–339, Mar. 2007, doi: 10.1016/j.amc.2006.07.128.


  • There are currently no refbacks.

Abava  Кибербезопасность IT congress 2023

ISSN: 2307-8162