Skip to main content
Springer Nature Link
Log in

Time Series Modeling Based on Fuzzy Transform

  • Conference paper
  • First Online:
Soft Methods for Data Science (SMPS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 456))

Included in the following conference series:

  • 1686 Accesses

Abstract

It is well known that smoothing is applied to better see patterns and underlying trends in time series. In fact, to smooth a data set means to create an approximating function that attempts to capture important features in the data, while leaving out noises. In this paper we choose, as an approximation function, the inverse fuzzy transform (introduced by Perfilieva in Fuzzy Sets Syst 157:993–1023, 2006 [3]) that is based on fuzzy partitioning of a closed real interval into fuzzy subsets. The empirical distribution we introduce can be characterized by its expectiles in a similar way as it is characterized by quantiles.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Di Martino F, Loia V, Sessa S (2010) Fuzzy transforms method and attribute dependency in data analysis. Inf Sci 180:493–505

    Article  MathSciNet  MATH  Google Scholar 

  2. Guerra ML, Stefanini L (2013) Expectile smoothing of time series using F-transform. In: Conference of the European society for fuzzy logic and technology, advances in intelligent systems research, vol 32, pp 559–564. ISBN: 978-162993219-4

    Google Scholar 

  3. Perfilieva I (2006) Fuzzy transforms: theory and applications. Fuzzy Sets Syst 157:993–1023

    Article  MathSciNet  MATH  Google Scholar 

  4. Perfilieva I (2006) Fuzzy transforms and their applications to data compression. In: Bloch I et al (eds) Fuzzy logic and applications, LNAI 3849. Springer, pp 19–31

    Google Scholar 

  5. Perfilieva I, Novak V, Dvorak A (2008) Fuzzy transform in the analysis of data. Int J Approx Reason 48:36–46

    Article  MATH  Google Scholar 

  6. Schnabel SK, Eilers PHC (2009) Optimal expectile smoothing. Comput Stat Data Anal 53:4168–4177

    Article  MathSciNet  MATH  Google Scholar 

  7. Stefanini L (2008) Fuzzy transform with parametric LU-fuzzy partitions. In: Ruan D et al (eds) Computational intelligence in decision and control. World Scientific, pp 399–404

    Google Scholar 

  8. Stefanini L (2009) Fuzzy transform and smooth functions. In: Carvalho JP, Dubois D, Kaymak U, Sousa JMC (eds) Proceeding of the IFSA-EUSFLAT 2009 conference, Lisbon, July 2009, pp 579–584

    Google Scholar 

  9. Stefanini L, Sorini L, Guerra ML (2006) Parametric representations of fuzzy numbers and application to fuzzy calculus. Fuzzy Sets Syst 157:2423–2455

    Article  MathSciNet  MATH  Google Scholar 

  10. Stefanini L, Sorini L, Guerra ML (2009) Fuzzy numbers and fuzzy arithmetic. In: Pedrycz W, Skowron A, Kreynovich V (eds) Handbook of granular computing, Chapter 12. Wiley

    Google Scholar 

  11. Stefanini L (2011) F-transform with parametric generalized fuzzy partitions. Fuzzy Sets Syst 180(1):98–120

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Economics, Society and Politics, University of Urbino, Urbino, Italy

    Luciano Stefanini & Laerte Sorini

  2. Department of Mathematics, University of Bologna, Bologna, Italy

    Maria Letizia Guerra

Authors
  1. Luciano Stefanini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laerte Sorini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maria Letizia Guerra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maria Letizia Guerra .

Editor information

Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maria Brigida Ferraro

  2. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Paolo Giordani

  3. Dept of Basic & Applied Sciences Engg, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  4. Dept of Stoc Metds,Polish Academy of Sci, Systems Research Institute, Warsaw, Poland

    Marek Gagolewski

  5. Dept of Statis&OR and MD, Univ de Oviedo, Oviedo, Spain

    María Ángeles Gil

  6. Dept of Stoc Metds,Polish Aca of Science, Systems Res Inst, Warsaw, Poland

    Przemysław Grzegorzewski

  7. Sys Res Inti, Dept of Stoch Methods, Polish Acadmy Sci in Warsaw, Warsaw, Poland

    Olgierd Hryniewicz

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this paper

Cite this paper

Stefanini, L., Sorini, L., Guerra, M.L. (2017). Time Series Modeling Based on Fuzzy Transform. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_57

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-42972-4_57

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42971-7

  • Online ISBN: 978-3-319-42972-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics