Skip to main content
SpringerLink
Log in

A Fuzzy Time Series Model with Customized Membership Functions

  • Conference paper
  • First Online:
Advances in Time Series Analysis and Forecasting (ITISE 2016)

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Included in the following conference series:

Abstract

In this study, a fuzzy time series modeling method that utilizes a class of customized and flexible parametric membership functions in the fuzzy rule consequents is introduced. The novelty of the proposed methodology lies in the flexibility of this membership function, which we call the composite kappa membership function, and its curve may take various shapes, such as a symmetric or asymmetric bell, triangular, or quasi trapezoid. In our approach, the fuzzy c-means clustering algorithm is used for fuzzification and for the establishment of fuzzy rule antecedents and a heuristic is introduced for identifying the quasi optimal number of clusters to be formed. The proposed technique does not require any preliminary parameter setting, hence it is easy-to-use in practice. In a real-life example, the modeling capability of the proposed method was compared to those of Winters’ method, the Autoregressive Integrated Moving Average technique and Adaptive Neuro-Fuzzy Inference System. Based on the empirical results, the proposed method may be viewed as a viable time series modeling technique.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)

    Book  MATH  Google Scholar 

  2. Calinski, T., Harabasz, J.: A dendrite method for cluster analysis. Commun. Stat. 3(1), 1–27 (1974)

    MathSciNet  MATH  Google Scholar 

  3. Cheng, C.H., Cheng, G.W., Wang, J.W.: Multi-attribute fuzzy time series method based on fuzzy clustering. Expert Syst. Appl. 34(2), 1235–1242 (2008)

    Article  MathSciNet  Google Scholar 

  4. Davies, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Trans. Pattern Anal. Mach. Intell. 1(2), 95–104 (1979)

    Google Scholar 

  5. Dombi, J.: Modalities. In: Eurofuse 2011. Advances in Intelligent and Soft Computing. Springer, London pp. 53–65 (2012)

    Google Scholar 

  6. Dombi, J.: On a certain type of unary operators. In: Proceedings of 2012 IEEE International Conference on Fuzzy Systems, Brisbane, QLD, pp. 1–7, 10–15 June 2012

    Google Scholar 

  7. Guillaume, S.: Designing fuzzy inference systems from data: an interpretability-oriented review. IEEE Trans. Fuzzy Syst. 9, 426–443 (2001)

    Article  Google Scholar 

  8. Huarng, K.: Heuristic models of fuzzy time series for forecasting. Fuzzy Sets Syst. 123, 369–386 (2001)

    Google Scholar 

  9. Hyndman, R., Khandakar, Y.: Automatic time series forecasting: the forecast package for r. J. Stati. Softw. 27 (2008). doi:10.18637/jss.v027.i03

  10. Kriegel, H., Kröger, P., Zimek, A.: Clustering high-dimensional data. ACM Trans. Knowl. Discov. Data 3(1) (2009). doi:10.1145/1497577.1497578

  11. Li, S.-T., Cheng, Y.-C., Lin, S.-Y.: A FCM-based deterministic forecasting model for fuzzy time series. Comput. Math. Appl. 56(12), 3052–3063 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Rousseeuw, P.J.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65 (1987)

    Article  MATH  Google Scholar 

  13. Singh, S.R.: A robust method of forecasting based on fuzzy time series. Appl. Math. Comput. 188(1), 472–484 (2007)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Štĕpnička, M., Dvořák, A., Pavliska, V., Vavříčková, L.: A linguistic approach to time series modeling with the help of F-transform. Fuzzy Sets Syst. 180(1), 164–184 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Waltz, R., Morales, J., Nocedal, J., Orban, D.: An interior algorithm for nonlinear optimization that combines line search and trust region steps. Math. Program. 9, 391–408 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Management and Corporate Economics, Budapest University of Technology and Economics, Magyar Tudósok Körútja 2, Budapest, 1117, Hungary

    Tamás Jónás & Zsuzsanna Eszter Tóth

  2. Institute of Informatics, University of Szeged, Árpád Tér 2, Szeged, 6720, Hungary

    József Dombi

Authors
  1. Tamás Jónás
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zsuzsanna Eszter Tóth
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. József Dombi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tamás Jónás .

Editor information

Editors and Affiliations

  1. CITIC-UGR, University of Granada, Granada, Spain

    Ignacio Rojas

  2. CITIC-UGR, University of Granada, Granada, Spain

    Héctor Pomares

  3. CITIC-UGR, University of Granada, Granada, Spain

    Olga Valenzuela

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Jónás, T., Eszter Tóth, Z., Dombi, J. (2017). A Fuzzy Time Series Model with Customized Membership Functions. In: Rojas, I., Pomares, H., Valenzuela, O. (eds) Advances in Time Series Analysis and Forecasting. ITISE 2016. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-55789-2_20

Download citation

Publish with us

Policies and ethics

Search

Navigation