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Toward a Restriction-Centered Theory of Truth and Meaning (RCT) Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Additive Fuzzy Systems as Generalized Probability Mixture Models

Author : Bart Kosko

Published in: Fifty Years of Fuzzy Logic and its Applications

Publisher: Springer International Publishing

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Abstract

Additive fuzzy systems generalize the popular mixture-density models of machine learning. Additive fuzzy systems map inputs to outputs by summing fired then-parts sets and then taking the centroid of the sum. This additive structure produces a simple convex structure: Outputs are convex combinations of the centroids of the fired then-part sets. Additive systems are uniform function approximators and admit simple learning laws that grow and tune rules from sample data. They also behave as conditional expectations with conditional variances and other higher moment that describe their uncertainty. But they suffer from exponential rule explosion in high dimensions. Extending finite-rule additive systems to fuzzy systems with continuum-many rules overcomes the problem of rule explosion if a higher-level mixture structure acts as a system of tunable meta-rules. Monte Carlo sampling can then compute fuzzy-system outputs.

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previous chapter Meta-Heuristic Optimization of a Fuzzy Character Recognizer
next chapter Fuzzy Information Retrieval Systems: A Historical Perspective
Literature
1.
Kosko, B.: Neural Networks and Fuzzy Systems, Prentice-Hall (1991)
2.
Kosko, B.: Fuzzy systems as universal approximators. IEEE Trans. Comput. 43(11), 1329–1333 (1994)CrossRefMATH
3.
Kosko, B.: Optimal fuzzy rules cover extrema. Int. J. Intell. Syst. 10, 249–255 (1995)CrossRef
4.
Dickerson, J.A., Kosko, B.: “Fuzzy Function Approximation with Ellipsoidal Rules”, with J.A. Dickerson. IEEE Trans. Syst. Man Cybern. 26(4), 542–560 (1996)CrossRef
5.
Kosko, B., Fuzzy Engineering. Prentice-Hall (1996)
6.
Kosko, B.: Global stability of generalized additive fuzzy systems. IEEE Trans. Syst. Man Cybern. 28(3), 441–452 (1998)CrossRef
7.
Mitaim, S., Kosko, B.: Neural fuzzy agents for profile learning and adaptive object matching. Presence 7(6), 617–637 (1998)CrossRef
8.
Mitaim, S., Kosko, B.: The shape of fuzzy sets in adaptive function approximation. IEEE Trans. Fuzzy Syst. 9(4), 637–656 (2001)CrossRef
9.
Lee, I., Anderson, W.F., Kosko, B.: Modeling of gunshot bruises in soft body armor with an adaptive fuzzy system. IEEE Trans. Syst. Man Cybern. 35(6), 1374–1390 (2005)CrossRef
10.
Kandel, A.: Fuzzy Mathematical Techniques with Applications. Addison-Wesley (1986)
11.
Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainty, and Information. Prentice-Hall (1988)
12.
Terano, T., Asai, A., Sugeno, M.: Fuzzy Systems Theory and its Applications. Academic Press (1992)
13.
Zimmerman, H.J.: Fuzzy Set Theory and its Application. Kluwer (1985)
14.
Isaka, S., Kosko, B.: Fuzzy Logic. Sci. Am. 269, 76–81 (1993)
15.
Jang, J.-S.R., Sun, C.-T.: Functional equivalence between radial basis function networks and fuzzy inference systems. IEEE Trans. Neural Netw. 4(1), 156–159 (1993)CrossRef
16.
Moody, J., Darken, C.: Fast learning in networks of locally tuned processing units. Neural Comput. 1, 281–294 (1989)CrossRef
17.
Specht, D.F.: A general regression neural network. IEEE Trans. Neural Netw. 4, 549–557 (1991)
18.
Wang, L.-X., Mendel, J.M.: Fuzzy basis functions, universal approximation, and orthogonal least-squares learning. IEEE Trans. Neural Netw. 3, 802–814 (1992)
19.
Watkins, F.A.: Fuzzy Engineering. Ph.D. Dissertation, Department of Electrical Engineering, UC Irvine, Irvine, CA (1994)
20.
Watkins, F.A.: The representation problem for additive fuzzy systems. In: Proceedings of the IEEE Int. Conference on Fuzzy Systems (IEEE FUZZ), vol. 1, pp. 117–122, March 1995
21.
Osoba, O., Mitaim, S., Kosko, B.: Bayesian inference with adaptive fuzzy priors and likelihoods. IEEE Trans. Syst. Man Cybern.-B 41(5), 1183–1197 (2011)CrossRef
22.
Osoba, O., Mitaim, S., Kosko, B.: Triply fuzzy function approximation for hierarchical bayesian inference. Fuzzy Optim. Decis. Making 11(3), 241–268 (2012)CrossRefMATHMathSciNet
23.
Hogg, R.V., McKean, J.W., Craig, A.T.: Introduction to Mathematical Statistics, 7th edn. Prentice Hall, New York (2013)
24.
Osoba, O., Mitaim, S., Kosko, B.: The noisy expectation-maximization algorithm. Fluctuation Noise Lett. 12(3), 1350012-1–1350012-30 (2013)
25.
Audhkhasi, K., Osoba, O., Kosko, B.: Noise benefits in backpropagation and deep bidirectional pre-training. In: Proceedings of the 2013 International Joint Conference on Neural Networks, pp. 2254–2261, August (2013)
26.
Audhkhasi, K., Osoba, O., Kosko, B.: Noise benefits in convolutional neural networks. In: Proceedings of the 2014 International Conference on Advances in Big Data Analytics, pp. 73–80, July (2014)
27.
Kong, S.G., Kosko, B.: “Adaptive fuzzy systems for backing up a truck-and- trailer”, with S.G. Kong. IEEE Trans. Neural Netw. 3(2), 211–223 (1992)CrossRef
28.
Cappe, O., Douc, R., Guillin, A., Marin, J.-M., Robert, C.P.: Adaptive importance sampling in general mixture classes. Stat Comput., 18(4), 447–459 (2008)
Metadata
Title
Additive Fuzzy Systems as Generalized Probability Mixture Models
Author
Bart Kosko
Copyright Year
2015
Book
Fifty Years of Fuzzy Logic and its Applications

Print ISBN: 978-3-319-19682-4

Electronic ISBN: 978-3-319-19683-1

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-19683-1_14

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