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.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
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)
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)
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)
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)
Yager, R.R.: A new approach to the summarization of data. Information Sciences 28, 69–86 (1982)
Kacprzyk, J., Yager, R.R.: Linguistic summaries of data using fuzzy logic. International Journal of General Systems 30, 33–154 (2001)
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)
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)
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)
Sklansky, J., Gonzalez, V.: Fast polygonal approximation of digitized curves. Pattern Recognition 12(5), 327–331 (1980)
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)
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)
Cross, V., Sudkamp, T.: Similarity and Compatibility in Fuzzy Set Theory: Assessment and Applications. Springer, Heidelberg (2002)
Kacprzyk, J., Zadrożny, S.: Linguistic database summaries and their protoforms: toward natural language based knowledge discovery tools. Information Sciences 173, 281–304 (2005)
Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Computers and Mathematics with Applications 9, 149–184 (1983)
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)
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)
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)
Author information
Authors and Affiliations
Editor information
Rights 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)