Skip to main content
SpringerLink
Log in

A modified weighted method of time series forecasting in intuitionistic fuzzy environment

  • Theoretical Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

In this paper, we present a modified weighted method of time series forecasting using intuitionistic fuzzy sets. The proposed weighted method provides a better approach to extent of the accuracy in forecasted outputs. As it is established that the length of interval plays a crucial role in forecasting the historical time series data, so a new technique is proposed to define the length of interval and the partition of the universe of discourse into unequal length of intervals. Further, triangular fuzzy sets are defined and obtain membership grades of each datum in historical time series data to their respective triangular fuzzy sets. Based on the score and accuracy function of intuitionistic fuzzy number, the historical time series data is intuitionistic fuzzified and assigned the weight for intuitionistic fuzzy logical relationship groups. Defuzzification technique is based on the defined intuitionistic fuzzy logical relationship groups and provides better forecasting accuracy rate. The proposed method is implemented to forecast the enrollment data at the University of Alabama and market share price of SBI at BSE India. The results obtained have been compared with other existing methods in terms of root mean square error and average forecasting error to show the suitability of the proposed method.

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 for forecasting based on type 2 fuzzy time series. Int. J. Model. Simul. 38(3), 180–188 (2017)

    Google Scholar 

  2. 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(4), 339–350 (2018)

    Google Scholar 

  3. Abhishekh, Gautam, S.S., Singh, S.R.: A score function based method of forecasting using intuitionistic fuzzy time series. New Math. Nat. Comput. 14(1), 91–111 (2018)

    Google Scholar 

  4. Abhishekh, Gautam, S.S., Singh, S.R.: A new type 2 fuzzy time series forecasting model based on three-factors fuzzy logical relationships. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 27(2), 251–276 (2019)

    Google Scholar 

  5. Abhishekh, Kumar, S.: Handling higher order time series forecasting approach in intuitionistic fuzzy environment. J. Control Decis. (2019). https://doi.org/10.1080/23307706.2019.1591310

    Article  Google Scholar 

  6. Askari, S.N., Montazerin, N., Zarandi, M.H.F.: A clustering based forecasting algorithm for multivariable fuzzy time series using linear combinations of independent variables. Appl. Soft Comput. 35, 151–160 (2015)

    Google Scholar 

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

    Google Scholar 

  8. Bas, E., Uslu, V.R., Yolcu, U., Egrioglu, E.: A fuzzy time series analysis approach by using differential evolution algorithm based on the number of recurrences of fuzzy relations. Am. J. Intell. Syst. 3, 75–82 (2013)

    Google Scholar 

  9. Bai, E., Wong, W.K., Chu, W.C., Xia, M., Pan, F.: A heuristic time-invariant model for fuzzy time series forecasting. Expert Syst. Appl. 38, 2701–2707 (2011)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  12. Chen, S.M.: Forecasting enrollments based on high-order fuzzy time series. Cybern. Syst. 33, 1–16 (2010)

    Google Scholar 

  13. Chen, S.M., Hsu, C.C.: A new method to forecast enrollments using fuzzy time series. Int. J. Appl. Sci. Eng. 2, 234–244 (2004)

    Google Scholar 

  14. Chen, S.M., Hwang, J.R.: Temperature prediction using fuzzy time series. IEEE Trans. Syst. Man Cybern. Part B Cybern. 30, 263–275 (2000)

    Google Scholar 

  15. Chen, S.M., Tan, J.M.: Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst. 67(2), 163–172 (1994)

    Google Scholar 

  16. Chen, S.M., Tanuwijaya, K.: Fuzzy forecasting based on high-order fuzzy logical relationships and automatic clustering techniques. Expert Syst. Appl. 38, 15425–15437 (2011)

    Google Scholar 

  17. Gautam, S.S., Abhishekh, : A novel moving average forecasting approach using fuzzy time series data set. J. Control Autom. Electr. Syst. 30, 532–544 (2019)

    Google Scholar 

  18. Gautam, S.S., Abhishekh, Singh, S.R.: A new high-order approach for forecasting fuzzy forecasting fuzzy time series data. Int. J. Comput. Intel. Appl. 17(4), 1850019-1–1850019-17 (2018)

    Google Scholar 

  19. Gautam, S.S., Abhishekh, Singh, S.R.: Topsis for multi criteria decision making in intuitionistic fuzzy environment. Int. J. Comput. Appl. 156(8), 42–49 (2016)

    Google Scholar 

  20. Grzegorzewski, P.: Distances and orderings in a family of intuitionistic fuzzy numbers. In: Proceedings of the Third Conference of the European Society for Fuzzy Logic and Technology EUSFLAT’ 2003, Zittau, 10–12 Sept 2003, pp 223–227 (2003)

  21. Hong, D.H., Choi, C.H.: Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst. 114(1), 103–113 (2000)

    Google Scholar 

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

    Google Scholar 

  23. 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)

    Google Scholar 

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

    Google Scholar 

  25. Jurio, A., Paternain, D., Bustince, H., Guerra, C., Beliakov, G.: A construction method of Atanassov intuitionistic fuzzy sets for image processing. In: Proceedings of the Fifth IEEE Conference on Intelligent Systems, pp. 337–342 (2010)

  26. Kumar, S., Gangwar, S.: Intuitionistic fuzzy time series: an approach for handling non-determinism in time series forecasting. IEEE Trans. Fuzzy Syst. 24, 1270–1281 (2015)

    Google Scholar 

  27. Sheng, T.L., Cheng, Y.C.: Deterministic fuzzy time series model for forecasting enrollments. Comput. Math Appl. 53, 1904–1920 (2007)

    Google Scholar 

  28. Singh, P., Borah, B.: An efficient time series forecasting model based on fuzzy time series. Eng. Appl. Artif. Intell. 26, 2443–2457 (2013)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  31. Singh, S.R.: A computational method of forecasting based on fuzzy time series. Math. Comput. Simul. 79, 539–554 (2008)

    Google Scholar 

  32. Singh, S.R.: A computational method of forecasting based on high-order fuzzy time series. Expert Syst. Appl. 36, 10551–10559 (2009)

    Google Scholar 

  33. Song, Q.: A note on fuzzy time series model selection with sample autocorrelation functions. Cybern. Syst. Int. J. 34, 93–107 (2003)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  37. Sullivan, J., Woodall, W.H.: A comparison of fuzzy forecasting and Markov modeling. Fuzzy Sets Syst. 64, 279–293 (1999)

    Google Scholar 

  38. Tsaur, R.C., Kuo, T.C.: The adaptive fuzzy time series model with an application to Taiwan tourism demand. Expert Syst. Appl. 38, 9164–9171 (2011)

    Google Scholar 

  39. Tsaur, R.Y., Yang, O.: Fuzzy relation analysis in fuzzy time series model. Comput. Math Appl. 49, 539–548 (2005)

    Google Scholar 

  40. Uslu, V.R., Bas, E., Yolcu, U., Egrioglu, E.: A fuzzy time series approach based on weights determined by the number of recurrences of fuzzy relations. Swarm Evol. Comput. 15, 19–26 (2014)

    Google Scholar 

  41. Ye, F., Zhang, L., Zhang, D., Fujita, H., Gong, Z.: A novel forecasting method based on multi-order fuzzy time series and technical analysis. Inf. Sci. 367–368, 41–57 (2016)

    Google Scholar 

  42. Yu, H.K.: Weighted fuzzy time series models for TAIEX forecasting. Phys. A 349, 609–624 (2005)

    Google Scholar 

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

    Google Scholar 

  44. Wang, Y., Lei, Y., Fan, X., Wang, Y.: Intuitionistic fuzzy time series forecasting model based on intuitionistic fuzzy reasoning. Math. Probl. Eng. 2016, 1–12 (2016)

    Google Scholar 

  45. Zadeh, L.A.: Fuzzy set. Inf. Control 8, 338–353 (1993)

    Google Scholar 

Download references

Acknowledgements

The authors express their gratitude to the editor and the anonymous reviewers for their insightful and constructive suggestions to improve the quality of this paper. First author is very thankful to her beloved wife Kirti Singh for their endless support to throughout the writing of this paper.

Author information

Authors and Affiliations

  1. Government Polytechnic College, Gariyaband, Chhattisgarh, India

    Surendra Singh Gautam

  2. Department of Mathematics, Vishwavidyalaya Engineering College, Ambikapur, Chhattisgarh, India

    Abhishekh

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

    S. R. Singh

Authors
  1. Surendra Singh Gautam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abhishekh
    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.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gautam, S.S., Abhishekh & Singh, S.R. A modified weighted method of time series forecasting in intuitionistic fuzzy environment. OPSEARCH 57, 1022–1041 (2020). https://doi.org/10.1007/s12597-020-00455-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-020-00455-8

Keywords

Search

Navigation