Skip to main content

Linguistic Summarization of Time Series by Using the Choquet Integral

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNAI,volume 4529)

Abstract

We further extend a new approach to a linguistic summarization of time series proposed in our previous works (cf. Kacprzyk, Wilbik and Zadrożny  [1,2,3,4,5]) in which we put forward the use of a fuzzy linguistic quantifier driven aggregation of trends (partial scores) via the traditional Zadeh calculus of linguistically quantified propositions and the Sugeno integral. Here we use for this purpose the Choquet integral that has been widely advocated for many decision analytic and economic problems. The results are intuitively appealing and the method is effective and efficient.

Keywords

  • Linguistic Term
  • Mean Absolute Deviation
  • Fuzzy Measure
  • Linguistic Label
  • Partial Score

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (Canada)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Kacprzyk, J., Wilbik, A., Zadrożny, S.: Linguistic summarization of trends: a fuzzy logic based approach. In: Proceedings of the 11th International Conference Information Processing and Management of Uncertainty in Knowledge-based Systems, Paris, France, July 2-7, 2006, pp. 2166–2172 (2006)

    Google Scholar 

  2. Kacprzyk, J., Wilbik, A., Zadrożny, S.: On some types of linguistic summaries of time series. In: Proceedings of the 3rd International IEEE Conference “Intelligent Systems”, London, UK, September 4-6, 2006, pp. 373–378. IEEE Press, Los Alamitos (2006)

    CrossRef  Google Scholar 

  3. Kacprzyk, J., Wilbik, A., Zadrożny, S.: A linguistic quantifier based aggregation for a human consistent summarization of time series. In: Lawry, J., Miranda, E., Bugarin, A., Li, S., Gil, M.A., Grzegorzewski, P., Hryniewicz, O. (eds.) Soft Methods for Integrated Uncertainty Modelling, pp. 186–190. Springer, Heidelberg (2006)

    Google Scholar 

  4. Kacprzyk, J., Wilbik, A., Zadrożny, S.: Capturing the essence of a dynamic behavior of sequences of numerical data using elements of a quasi-natural language. In: Proceedings of the 2006 IEEE International Conference on Systems, Man, and Cybernetics, Taipei, Taiwan, October 8-11, 2006, pp. 3365–3370. IEEE Press, Los Alamitos (2006)

    CrossRef  Google Scholar 

  5. Kacprzyk, J., Wilbik, A., Zadrożny, S.: Linguistic summaries of time series via a quantifier based aggregation using the Sugeno integral. In: Proceedings of 2006 IEEE World Congress on Computational Intelligence, Vancouver, BC, Canada, July 16-21, 2006, pp. 3610–3616. IEEE Press, Los Alamitos (2006)

    Google Scholar 

  6. Yager, R.R.: A new approach to the summarization of data. Information Sciences 28, 69–86 (1982)

    CrossRef  MATH  MathSciNet  Google Scholar 

  7. Kacprzyk, J., Yager, R.R.: Linguistic summaries of data using fuzzy logic. International Journal of General Systems 30, 33–154 (2001)

    CrossRef  MathSciNet  Google Scholar 

  8. Kacprzyk, J., Yager, R.R., Zadrożny, S.: A fuzzy logic based approach to linguistic summaries of databases. International Journal of Applied Mathematics and Computer Science 10, 813–834 (2000)

    MATH  Google Scholar 

  9. Narukawa, Y., Murofushi, T.: Choquet integral and Sugeno integral as aggregation function. In: Torra, V. (ed.) Information Fusion in Data Mining, pp. 27–39. Springer, Heidelberg (2003)

    Google Scholar 

  10. Narukawa, Y., Murofushi, T., Torra, V.: Decision modelling using the Choquet integral. In: Torra, V., Narukawa, Y. (eds.) MDAI 2004. LNCS (LNAI), vol. 3131, pp. 183–193. Springer, Heidelberg (2004)

    Google Scholar 

  11. Sklansky, J., Gonzalez, V.: Fast polygonal approximation of digitized curves. Pattern Recognition 12(5), 327–331 (1980)

    CrossRef  Google Scholar 

  12. Batyrshin, I.: On granular derivatives and the solution of a granular initial value problem. International Journal Applied Mathematics and Computer Science 12(3), 403–410 (2002)

    MATH  Google Scholar 

  13. Batyrshin, I., Sheremetov, L.: Perception based functions in qualitative forecasting. In: Batyrshin, I., Kacprzyk, J., Sheremetov, L., Zadeh, L.A. (eds.) Perception-based Data Mining and Decision Making in Economics and Finance, Springer, Heidelberg (2006)

    Google Scholar 

  14. Cross, V., Sudkamp, T.: Similarity and Compatibility in Fuzzy Set Theory: Assessment and Applications. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  15. Kacprzyk, J., Zadrożny, S.: Linguistic database summaries and their protoforms: toward natural language based knowledge discovery tools. Information Sciences 173, 281–304 (2005)

    CrossRef  MathSciNet  Google Scholar 

  16. Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Computers and Mathematics with Applications 9, 149–184 (1983)

    CrossRef  MATH  MathSciNet  Google Scholar 

  17. Zadeh, L.A.: A prototype-centered approach to adding deduction capabilities to search engines – the concept of a protoform. In: Proceedings of the Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS 2002), pp. 523–525 (2002)

    Google Scholar 

  18. Grabisch, M.: Fuzzy integral as a flexible and interpretable tool of aggregation. In: Bouchon-Meunier, B. (ed.) Aggregation and Fusion of Imperfect Information, pp. 51–72. Physica-Verlag, Heidelberg (1998)

    Google Scholar 

  19. Bosc, P., Lietard, L., Pivet, O.: Quantified statements and database fuzzy queries. In: Bosc, P., Kacprzyk, J. (eds.) Fuzziness in Database Management Systems, Springer, Heidelberg (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Patricia Melin Oscar Castillo Luis T. Aguilar Janusz Kacprzyk Witold Pedrycz

Rights and permissions

Reprints and Permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Kacprzyk, J., Wilbik, A., Zadrożny, S. (2007). Linguistic Summarization of Time Series by Using the Choquet Integral. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72950-1_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72917-4

  • Online ISBN: 978-3-540-72950-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics