Abstract
System modeling in dynamic environments needs processing of streams of sensor data and incremental learning algorithms. This paper suggests an incremental granular fuzzy rule-based modeling approach using streams of fuzzy interval data. Incremental granular modeling is an adaptive modeling framework that uses fuzzy granular data that originate from unreliable sensors, imprecise perceptions, or description of imprecise values of a variable in the form fuzzy intervals. The incremental learning algorithm builds the antecedent of functional fuzzy rules and the rule base of the fuzzy model. A recursive least squares algorithm revises the parameters of a state-space representation of the fuzzy rule consequents. Imprecision in data is accounted for using specificity measures. An illustrative example concerning the Rossler attractor is given.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 90, 111–127 (1997)
Bouchon-Meunier, B. et al. (ed.): Uncertainty in Intelligent and Information Systems. World Scientific, Singapore (2008)
Zadeh, L.A.: Generalized theory of uncertainty - principal concepts and ideas. Comp. Stats Data Anal. 51, 15–46 (2006)
Leite, D., Ballini, R., Costa, P., Gomide, F.: Evolving fuzzy granular modeling from nonstationary fuzzy data streams. Evolving Syst. 3(2), 65–79 (2012)
Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. Wiley, Chichester (2008)
Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Boston (2002)
Pedrycz, W., Gomide, F.: Fuzzy Systems Engineering: Toward Human-Centric Computing. Wiley, Hoboken (2007)
Leite, D., Costa, P., Gomide, F.: Evolving granular neural networks from fuzzy data streams. Neural Netw. 38, 1–16 (2012)
Leite, D., Palhares, R., Campos, V., Gomide, F.: Evolving granular fuzzy model-based control of nonlinear dynamic systems. IEEE Trans. Fuzzy Syst. 17 (2014). doi:10.1109/TFUZZ.2014.2333774
Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions: A Guide for Practitioners. Springer, Berlin (2007)
Yager, R.R.: Learning from imprecise granular data using trapezoidal fuzzy set representations. In: Prade, H., Subrahmanian, V.S. (eds.) LNCS, vol. 4772, pp. 244–254. Springer, Berlin (2007)
Cross, V.V., Sudkamp, T.A.: Similarity and Compatibility in Fuzzy Set Theory: Assessment and Applications. Physica-Verlag, Heidelberg (2002)
Yager, R.R.: Measures of specificity over continuous spaces under similarity relations. Fuzzy Sets Syst. 159, 2193–2210 (2008)
Young, P.C.: Recursive Estimation and Time-Series Analysis: An Introduction. Springer, Berlin (1984)
Astrom, K.J., Wittenmark, B.: Adaptive Control. Addison-Wesley Publishing Company, Lund Institute of Technology (1989)
Johnson, C.R.: Lectures on Adaptive Parameter Estimation. Prentice-Hall, Upper Saddle River (1988)
Rossler, O.E.: An equation for continuous chaos. Phys. Lett. 57A(5), 397–398 (1976)
Angelov, P., Filev, D.: Simpl-eTS: a simplified method for learning evolving Takagi-Sugeno fuzzy models. In: IEEE International Conference on Fuzzy Systems, pp. 1068–1073 (2005)
Kasabov, N., Song, Q.: DENFIS: dynamic evolving neural-fuzzy inference system and its application for time-series prediction. IEEE Trans. Fuzzy Syst. 10–2, 144–154 (2002)
Angelov, P., Zhou, X.: Evolving fuzzy systems from data streams in real-time. In: International Symposium on Evolving Fuzzy Systems, pp. 29–35 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Leite, D., Gomide, F. (2015). Incremental Granular Fuzzy Modeling Using Imprecise Data Streams. In: Tamir, D., Rishe, N., Kandel, A. (eds) Fifty Years of Fuzzy Logic and its Applications. Studies in Fuzziness and Soft Computing, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-319-19683-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-19683-1_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19682-4
Online ISBN: 978-3-319-19683-1
eBook Packages: EngineeringEngineering (R0)