Skip to main content
SpringerLink
Log in

A refined method of forecasting based on high-order intuitionistic fuzzy time series data

  • Regular Paper
  • Published:
Progress in Artificial Intelligence Aims and scope Submit manuscript

Abstract

In this paper, we present a refined method of forecasting based on high-order intuitionistic fuzzy time series by transformed a historical fuzzy time series data into intuitionistic fuzzy time series data via defining their appropriate membership and non-membership function. The fuzzification of historical time series data is intuitionistic fuzzification which is based on their score and accuracy function. Also intuitionistic fuzzy logical relationship groups are defined and introduced a defuzzification process for high-order intuitionistic fuzzy time series. The aim of this paper is to propose an idea of high-order intuitionistic fuzzy time series which is generalization of fuzzy time series models and its experimental result shows that the proposed high-order intuitionistic fuzzy forecasting method gets better forecasting accuracy rates over the existing methods. The proposed method has been implemented on the historical enrollment data at the University of Alabama. The comparison result of these illustration shows that the proposed method has smaller forecasting accuracy rates in terms of MSE and MAPE over than the existing models in fuzzy time series.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Abhishekh, Gautam, S.S., Singh S.R.: A refined weighted method for forecasting based on type 2 fuzzy time series. Int. J. Model. Simul. https://doi.org/10.1080/02286203.2017.1408948 (2017)

    Article  Google Scholar 

  2. Abhishekh, Kumar, S.: A computational method for rice production forecasting based on high-order fuzzy time series. Int. J. Fuzzy Math. Arch. 13, 145–157 (2017)

  3. Abhishekh, Gautam, S.S., Singh, S.R.: A score function based method of forecasting using intuitionistic fuzzy time series. New Math. Natl. Comput. 14(1), 1–21 (2018)

    Article  MathSciNet  Google Scholar 

  4. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)

    Article  Google Scholar 

  5. Bahrami, B., Shafiee, M.: Fuzzy descriptor models for earthquake time prediction using seismic time series. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 23, 505–519 (2015)

    Article  MathSciNet  Google Scholar 

  6. Bas, E., Uslu, V.R., Yolcu, U., Egrioglu, E.: A modified genetic algorithm for forecasting fuzzy time series. Appl. Intell. 41, 453–463 (2016)

    Article  Google Scholar 

  7. Bisht, K., Kumar, S.: Fuzzy time series forecasting method based on hesitant fuzzy sets. Expert Syst. Appl. 64, 557–568 (2016)

    Article  Google Scholar 

  8. Cai, Q., Zhang, D., Wu, B., Leung, S.C.H.: A novel stock forecasting model based on fuzzy time series and genetic algorithm. Procedia Comput. Sci. 18, 1155–1162 (2013)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  11. Gangwar, S.S., Kumar, S.: Probabilistic and intuitionistic fuzzy sets-based method for fuzzy time series forecasting. Cybern. Syst. Int. J. 45, 349–361 (2014)

    Article  Google Scholar 

  12. Gani, A.N., Assarudeen, S.N.M.: A new operation on triangular fuzzy number for solving fuzzy linear programming problem. Appl. Math. Sci. 6, 525–532 (2012)

    MathSciNet  MATH  Google Scholar 

  13. Gautam, S.S., Abhishekh, Singh, S.R.: An improved-based TOPSIS method in interval valued intuitionistic fuzzy environment. Life Cycle Reliab. Saf. Eng. https://doi.org/10.1007/s41872-018-0042-z (2018)

    Article  Google Scholar 

  14. Huarng, K.H.: Effectives length of intervals to improve forecasting in fuzzy time series. Fuzzy Sets Syst. 123, 387–394 (2001)

    Article  MathSciNet  Google Scholar 

  15. Huang, Y.L.: A hybrid forecasting model for enrollments based on aggregated fuzzy time series and particle swarm optimization. Expert Syst. Appl. 38, 8014–8023 (2011)

    Article  Google Scholar 

  16. Hsu, Y.Y., Tse, S.M., Wu, B.: A new approach of bivrate fuzzy time series analysis to the forecasting of a stock index. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 11, 671–690 (2003)

    Article  Google Scholar 

  17. Joshi, B.P., Kumar, S.: Intuitionistic fuzzy sets based method for fuzzy time series forecasting. Cybern. Syst. Int. J. 43, 34–47 (2012)

    Article  Google Scholar 

  18. Jurio, A., Paternain, H., Guerra, C., Beliakov, G.: A construction method of atanassov’s intuitionistic fuzzy sets for image processing. In: Paper Presented at the Intelligent Systems (IS), 5th IEEE International Conference London, 7–9, July (2010)

  19. Kumar, S., Gangwar, S.S.: Intuitionistic fuzzy time series: an approach for handling nondeterminism in time series forecasting. IEEE Trans. Fuzzy Syst. 24, 1270–1281 (2016)

    Article  Google Scholar 

  20. Kumar, S., Gangwar, S.S.: A fuzzy time series forecasting method induced by intuitionistic fuzzy sets. Int. J. Model. Simul. Sci. Comput. 6, 23 (2015)

    Article  Google Scholar 

  21. Lee, H.S., Chou, M.T.: Fuzzy forecasting based on fuzzy time series. Int. J. Comput. Math. 81, 781–789 (2004)

    Article  MathSciNet  Google Scholar 

  22. Singh, S.R.: A simple method of forecasting based on fuzzy time series. Appl. Math. Comput. 186, 330–339 (2007)

    MathSciNet  MATH  Google Scholar 

  23. Singh, S.R.: A robust method of forecasting based on fuzzy time series. Appl. Math. Comput. 188, 472–484 (2007)

    MathSciNet  MATH  Google Scholar 

  24. Singh, S.R.: A simple time variant method for fuzzy time series forecasting. Cybern. Syst. Int. J. 38, 305–321 (2007)

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Song, Q., Chissom, B.S.: Forecasting enrollments with fuzzy time series-Part II. Fuzzy Sets Syst. 64, 1–8 (1994)

    Article  Google Scholar 

  27. Tsaur, R.C., Yang, J.C.O., Wang, H.F.: Fuzzy relation analysis in fuzzy time series model. Comput. Math. Appl. 49, 539–548 (2005)

    Article  MathSciNet  Google Scholar 

  28. Wang, Y., Lei, Y., Wang, Y., Zheng, K.: A heuristic adaptive-order intuitionistic fuzzy time series forecasting model. J. Electron. Inf. Technol. 38, 2795–2802 (2016)

    Google Scholar 

  29. Wang, Y., Lei, Y., Fan, X., Wang, Y.: Intuitionistic fuzzy time series forecasting model based on intuitionistic fuzzy reasoning. Hindawi Publ. Corp. Math. Probl. Eng. 10, 5035160–5035172 (2016)

    MathSciNet  MATH  Google Scholar 

  30. Xu, Z.S., Yager, R.R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen. Syst. 35, 417–433 (2006)

    Article  MathSciNet  Google Scholar 

  31. Xu, Z.S.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15, 1179–1187 (2007)

    Article  Google Scholar 

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

    Article  Google Scholar 

Download references

Acknowledgements

The authors are very thankful to the reviewers for their constructive suggestion to enhance the quality of this paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India

    Abhishekh, Surendra Singh Gautam & S. R. Singh

Authors
  1. Abhishekh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Surendra Singh Gautam
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. R. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abhishekh.

Ethics declarations

Conflict of interest

The authors declare that they have no any conflict of interests.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abhishekh, Gautam, S.S. & Singh, S.R. A refined method of forecasting based on high-order intuitionistic fuzzy time series data. Prog Artif Intell 7, 339–350 (2018). https://doi.org/10.1007/s13748-018-0152-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13748-018-0152-x

Keywords

Search

Navigation