A Novel Moving Average Forecasting Approach Using Fuzzy Time Series Data Set

Abstract

In this study, we develop a novel moving average forecasting approach based on fuzzy time series data set. The main objective of applying this moving average approach in develop method is to provide better results and enhance the accuracy in forecasted output by reducing the fluctuation in time series data set. The developed method is to define the universe of discourse and partition into equal length of intervals which is based on the average-length method. Further, triangular fuzzy sets are defined and obtain a membership grade of each moving average historical datum rather than actual datum of historical fuzzy time series data. Here, the fuzzification process of moving average historical data to their maximum membership grades obtained into corresponding triangular fuzzy sets. The general suitability of developed model has been examined by implementing in the forecast of student enrollments data at the University of Alabama. Further, the market price of State Bank of India share at Bombay Stock Exchange, India, has also been implemented in the forecast. The developed method of moving average fuzzy time series provides an improved forecasted output with least root mean square error and average forecasting errors which shows that our developed method is more superior than other existing models available in the literature based on fuzzy time series data.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3

References

  1. Abhishekh, Bharati, S. K., & Singh, S. R. (2019). A novel approach to handle forecasting problems based on moving average two-factor fuzzy time series. In J. C. Bansal, K. N. Das, A. Nagar, K. Deep, & A. K. Ojha Soft computing for problem solving; Advances in intelligent systems and computing (Vol. 816). Singapore: Springer.

    Google Scholar 

  2. Abhishekh, Gautam, S. S., & Singh, S. R. (2017). A refined weighted for forecasting based on type 2 fuzzy time series. International Journal of Modelling and Simulation, 38, 180–188.

    Article  Google Scholar 

  3. Abhishekh, Gautam, S. S., & Singh, S. R. (2018a). A score function based method of forecasting using intuitionistic fuzzy time series. New Mathematics and Natural Computation, 14(1), 91–111.

    MathSciNet  Article  Google Scholar 

  4. Abhishekh, Gautam, S. S., & Singh, S. R. (2018b). A refined method of forecasting based on high-order intuitionistic fuzzy time series data. Progress in Artificial Intelligence, 7(4), 339–350.

    Article  Google Scholar 

  5. Abhishekh, & Kumar, S. (2017). A computational method for rice production forecasting based on high-order fuzzy time series. International Journal of Fuzzy Mathematical Archive, 13(2), 145–157.

    Google Scholar 

  6. Aladag, C. H., Basaran, M. A., Egrioglu, E., Yolcu, U., & Uslu, V. R. (2009). Forecasting in high order fuzzy time series by using neural networks to define fuzzy relations. Expert Systems with Applications, 36, 4228–4231.

    Article  Google Scholar 

  7. Aladag, C. H., Yolcu, U., Egrioglu, E., & Dalar, A. Z. (2012). A new time invariant fuzzy time series forecasting method based on particle swarm optimization. Applied Soft Computing, 12(10), 3291–3299.

    Article  Google Scholar 

  8. Bisht, K., & Kumar, S. (2016). Fuzzy time series forecasting method based on hesitant fuzzy sets. Expert Systems with Applications, 64, 557–568.

    Article  Google Scholar 

  9. Chang, X. H., Li, Z. M., & Park, J. H. (2017a). Fuzzy generalized H2 filtering for nonlinear discrete-time systems with measurements quantization. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 99, 1–12.

    Google Scholar 

  10. Chang, X. H., Park, J. H., & Shi, P. (2017b). Fuzzy resilient energy-to-peak filtering for continuous-time nonlinear systems. IEEE Transactions on Fuzzy Systems, 25(6), 1576–1588.

    Article  Google Scholar 

  11. Chang, X. H., & Wang, Y. M. (2018). Peak to peak filtering for networked nonlinear DC motor systems with quantization. IEEE Transactions on Industrial Informatics, 14(12), 5378–5388.

    Article  Google Scholar 

  12. Chen, S. M. (1996). Forecasting enrollments based on fuzzy time series. Fuzzy Sets and Systems, 81(3), 311–319.

    MathSciNet  Article  Google Scholar 

  13. Chen, S. M. (2002). Forecasting enrollments based on high-order fuzzy time series. Cybernetics and Systems, 33(1), 1–16.

    MATH  Article  Google Scholar 

  14. Chen, S. M., & Chung, N. Y. (2006). Forecasting enrollments using high-order fuzzy time series and genetic algorithms. International Journal of Intelligent Systems, 21(5), 485–501.

    MATH  Article  Google Scholar 

  15. Chen, S. M., & Hsu, C. C. (2004). A new method to forecast enrollments using fuzzy time series. International Journal of Applied Science and Engineering, 2(3), 234–244.

    Google Scholar 

  16. Chen, S. M., & Kao, P. Y. (2013). TAIEX forecasting based on fuzzy time series, particle swarm optimization techniques and support vector machines. Information Sciences, 247, 62–71.

    MathSciNet  Article  Google Scholar 

  17. Chen, S. M., & Tanuwijaya, K. (2011). Fuzzy forecasting based on high-order fuzzy logical relationships and automatic clustering techniques. Expert Systems with Applications, 38, 15425–15437.

    Article  Google Scholar 

  18. Chen, S. M., Wang, N. Y., & Pan, J. S. (2009). Forecasting enrollments using automatic clustering techniques and fuzzy logical relationships. Expert Systems with Applications, 36(8), 11070–11076.

    Article  Google Scholar 

  19. Eǧrioǧlu, E. (2012). A new time-invariant fuzzy time series forecasting method based on genetic algorithm. Advances in Fuzzy Systems, 2012, 785709. https://doi.org/10.1155/2012/785709.

    MathSciNet  MATH  Article  Google Scholar 

  20. Fraccaroli, F., Peruffo, A., & Zorzi, M. A. (2015). A new recursive least-squares method with multiple forgetting schemes. In: 2015 54th IEEE conference on decision and control (CDC) (pp. 3367–3372).

  21. Gangwar, S. S., & Kumar, S. (2012). Partitions based computational method for high-order fuzzy time series forecasting. Expert Systems with Applications, 39(15), 12158–12164.

    Article  Google Scholar 

  22. Gangwar, S. S., & Kumar, S. (2014). Probabilistic and intuitionistic fuzzy sets-based method for fuzzy time series forecasting. Cybernetics and Systems, 45(4), 349–361.

    MATH  Article  Google Scholar 

  23. Gangwar, S. S., & Kumar, S. (2015). Computational method for high-order weighted fuzzy time series forecasting based on multiple partitions. In M. Chakraborty, A. Skowron, M. Maiti, & S. Kar (Eds.), Facets of uncertainties and applications (pp. 293–302). New Delhi: Springer.

    Google Scholar 

  24. Gautam, S. S., Abhishekh, & Singh, S. R. (2018a). An improved-based TOPSIS method in interval valued intuitionistic fuzzy environment. Life Cycle Reliability and Safety Engineering, 7, 81–88.

    Article  Google Scholar 

  25. Gautam, S. S., Abhishekh, & Singh, S. R. (2018b). An intuitionistic fuzzy soft set theoretic approach to decisions making problems. MATEMATIKA, 34, 49–58.

    Article  Google Scholar 

  26. Gautam, S. S., Abhishekh, & Singh, S. R. (2018c). A new high-order approach for forecasting fuzzy time series data. International Journal of Computational Intelligence and Applications, 17, 1850019.

    Article  Google Scholar 

  27. Huarng, K. (2001). Effective lengths of intervals to improve forecasting in fuzzy time series. Fuzzy Sets and Systems, 123(3), 387–394.

    MathSciNet  MATH  Article  Google Scholar 

  28. Huarng, K., & Yu, T. H. (2006). Ratio-based lengths of intervals to improve fuzzy time series forecasting. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 36(2), 328–340.

    Article  Google Scholar 

  29. Huo, X., Ma, L., Zhao, X., & Zong, G. (2019). Observer-based fuzzy adaptive stabilization of uncertain switched stochastic nonlinear systems with input quantization. Journal of the Franklin Institute, 356, 1789–1809.

    MathSciNet  MATH  Article  Google Scholar 

  30. Hwang, J. R., Chen, S. M., & Lee, C. H. (1998). Handling forecasting problems using fuzzy time series. Fuzzy Sets and Systems, 100(1–3), 217–228.

    Article  Google Scholar 

  31. Jilani, T. A., & Burney, S. M. (2008). Multivariate stochastic fuzzy forecasting models. Expert Systems with Applications, 35(3), 691–700.

    Article  Google Scholar 

  32. Lee, H. S., & Chou, M. T. (2004). Fuzzy forecasting based on fuzzy time series. International Journal of Computer Mathematics, 81(7), 781–789.

    MathSciNet  MATH  Article  Google Scholar 

  33. Lee, L. W., Wang, L. H., Chen, S. M., & Leu, Y. H. (2006). Handling forecasting problems based on two-factors high-order fuzzy time series. IEEE Transactions on Fuzzy Systems, 14(3), 468–477.

    Article  Google Scholar 

  34. Li, S. T., & Cheng, Y. C. (2007). Deterministic fuzzy time series model for forecasting enrollments. Computers & Mathematics with Applications, 53(12), 1904–1920.

    MathSciNet  MATH  Article  Google Scholar 

  35. Pathak, H. K., & Singh, P. (2011). A new bandwidth interval based forecasting method for enrollments using fuzzy time series. Applied Mathematics, 2(04), 504.

    Article  Google Scholar 

  36. Qiu, W., Liu, X., & Li, H. (2011). A generalized method for forecasting based on fuzzy time series. Expert Systems with Applications, 38(8), 10446–10453.

    Article  Google Scholar 

  37. Singh, S. R. (2007a). A simple method of forecasting based on fuzzy time series. Applied Mathematics and Computation, 186(1), 330–339.

    MathSciNet  MATH  Article  Google Scholar 

  38. Singh, S. R. (2007b). A robust method of forecasting based on fuzzy time series. Applied Mathematics and Computation, 188(1), 472–484.

    MathSciNet  MATH  Article  Google Scholar 

  39. Song, Q. (2003). A note on fuzzy time series model selection with sample autocorrelation functions. Cybernetics & Systems, 34(2), 93–107.

    MATH  Article  Google Scholar 

  40. Song, Q., & Chissom, B. S. (1993). Forecasting enrollments with fuzzy time series—Part I. Fuzzy Sets and Systems, 54(1), 1–9.

    Article  Google Scholar 

  41. Song, Q., & Chissom, B. S. (1994). Forecasting enrollments with fuzzy time series—Part II. Fuzzy Sets and Systems, 62(1), 1–8.

    Article  Google Scholar 

  42. Wang, N. Y., & Chen, S. M. (2009). Temperature prediction and TAIFEX forecasting based on automatic clustering techniques and two-factors high-order fuzzy time series. Expert Systems with Applications, 36(2), 2143–2154.

    Article  Google Scholar 

  43. Wang, Y., Lei, Y., Fan, X., & Wang, Y. (2016). Intuitionistic fuzzy time series forecasting model based on intuitionistic fuzzy reasoning. Mathematical Problems in Engineering, 2016, 5035160. https://doi.org/10.1155/2016/5035160.

    MathSciNet  MATH  Article  Google Scholar 

  44. Wong, W. K., Bai, E., & Chu, A. W. (2010). Adaptive time-variant models for fuzzy time series forecasting. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 40(6), 1531–1542.

    Article  Google Scholar 

  45. Yolcu, U., Egrioglu, E., Uslu, V. R., Basaran, M. A., & Aladag, C. H. (2009). A new approach for determining the length of intervals for fuzzy time series. Applied Soft Computing, 9(2), 647–651.

    MATH  Article  Google Scholar 

  46. Yu, H. K. (2005). A refined fuzzy time-series model for forecasting. Physica A: Statistical Mechanics and Its Applications, 346(3), 657–681.

    Article  Google Scholar 

  47. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.

    MathSciNet  MATH  Article  Google Scholar 

  48. Zhao, X., Shi, P., & Zheng, X. (2016). Fuzzy adaptive control design and discretization for a class of nonlinear uncertain systems. IEEE Transactions on Cybernetics, 46(6), 1476–1483.

    Article  Google Scholar 

Download references

Acknowledgements

The authors are very thankful to the editor and the anonymous reviewers for their constructive suggestions and comments to enhance the quality of the study.

Author information

Affiliations

Authors

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

Verify currency and authenticity via CrossMark

Cite this article

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). https://doi.org/10.1007/s40313-019-00467-w

Download citation

Keywords

  • Fuzzy time series
  • Triangular fuzzy number
  • Fuzzy logical relationships
  • Moving average data
  • Market prices of BSE