Abstract
We concentrate on Takagi—Sugeno (TS) probabilistic fuzzy systems where interpretability of fuzzy systems is combined with the statistical properties of probabilistic systems. After having sketched the general architecture of TS probabilistic fuzzy systems, we present an appropriate mathematical framework and introduce two probabilistic fuzzy reasoning schemes which have a different interpretation but, eventually, yield the same input-output mapping. We illustrate our theoretical considerations by presenting some simulation results concerning a financial time series analysis.
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 subscriptionsPreview
Unable to display preview. Download preview PDF.
References
G. J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: theory and applications, Prentice Hall, Upper Saddle River, 1995.
Mohammad Jamshidi, André Titli, Lotfi Zadeh, and Serge Boverie, Eds., Applications of Fuzzy Logic, Prentice Hall, New Jersey, 1997.
E. H. Mamdani, “Application of fuzzy logic to approximate reasoning using linguistic systems,” IEEE Transactions on Computers, vol. 26, no. 12, pp. 11821191, 1977.
Serge Guillaume, “Designing fuzzy inference systems from data: an interpretability-oriented review,” IEEE Transactions on Fuzzy Systems, vol. 9, no. 3, pp. 426–443, June 2001.
V. Kecman, Learning and Soft Computing, MIT Press, Cambridge, MA, 2001.
Jan van den Berg, Willem Max van den Bergh, and Uzay Kaymak, “Probabilistic and statistical fuzzy set foundations of competitive exception learning,” in Proceedings of the Tenth IEEE International Conference on Fuzzy Systems, Melbourne, Australia, Melbourne, 2001, vol. 2, pp. 1035–1038.
L. A. Zadeh, “Probability measures and fuzzy events,” in Fuzzy Sets and Applications, Selected Papers by L.A. Zadeth, R.R. Yager, S. Ovchinnikov, R.M Tong, and H.T. Nguyen, Eds., pp. 45–51. John Wiley and Sons, USA, 1987.
J. C. Hull, Options, Futures, Other Derivatives, Prentice Hall, Upper Saddle River, 4-th edition, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
van den Berg, J., Kaymak, U., van den Bergh, WM. (2002). Probabilistic Reasoning in Fuzzy Rule-Based Systems. In: Grzegorzewski, P., Hryniewicz, O., Gil, M.Á. (eds) Soft Methods in Probability, Statistics and Data Analysis. Advances in Intelligent and Soft Computing, vol 16. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1773-7_18
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1773-7_18
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1526-9
Online ISBN: 978-3-7908-1773-7
eBook Packages: Springer Book Archive