×

Deriving prediction intervals for neuro-fuzzy networks. (English) Zbl 1090.90018

Summary: We describe a method to derive prediction intervals for neuro-fuzzy networks used as predictive systems. The method also enables the definition of prediction intervals for the fuzzy rules that constitute the rule base of the neuro-fuzzy network, resulting in a more readable and robust knowledge base. Moreover, the method does not depend on a specific architecture and can be applied to a variety of neuro-fuzzy models. An illustrative example and a real-world case study are reported to show the effectiveness of the proposed method.

MSC:

90B10 Deterministic network models in operations research
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming

Software:

bootstrap; ANFIS
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Zadeh, L., A new approach to the analysis of complex systems, IEEE Trans. on System, Man and Cybernetics, 3, 1 (1973)
[2] Bargiela, A.; Pedrycz, W., Granular Computing: An Introduction (2003), Kluwer Academic Publishers: Kluwer Academic Publishers Baltimore, MD · Zbl 1046.68052
[3] Pedrycz, W.; Gomide, F., An Introduction to Fuzzy Sets: Analysis and Design (1998), The MIT Press · Zbl 0938.03078
[4] Farinwata, S. S.; Filev, D.; Langari, R., Fuzzy Control: Synthesis and Analysis (2000), Wiley · Zbl 0935.00024
[5] Ross, T. J., Fuzzy Logic with Engineering Applications (1997), McGraw Hill Int. Ed.
[6] Jang, J.-S. R.; Sun, C.-T., Neuro-fuzzy modeling and control, (Proceedings of the IEEE (1995))
[7] Nauck, D.; Klawonn, F.; Kruse, R., Foundations of Neuro-Fuzzy Systems (1997), Wiley
[8] Dybowski, R.; Roberts, S., Confidence intervals and prediction intervals for feed-forward neural networks, (Dybowski, R.; Gant, V., Clinical Applications of Artificial Neural Networks (2001), Cambridge University Press: Cambridge University Press Chichester), 298-326
[9] Papadopoulos, G.; Edwards, P. J.; Murray, A. F., Confidence estimation for neural networks: A practical comparison, IEEE Trans. On Neural Networks, 12, 6 (2001)
[10] Ungar, L. H.; De Veaux, R. D.; Rosengarten, E., Estimating prediction intervals for artificial neural networks, (Ninth Yale Workshop on Adaptive and Learning Systems (1996))
[11] Nix, D. A.; Weigend, A. S., Learning local error bars for nonlinear regression, (Tesauro, G.; Touretzky, D.; Leen, T., Advances in Neural Information Processing Systems 7 (1994), MIT Press: MIT Press Cambridge), 489-496
[12] Heskes, T., Practical confidence and prediction intervals, (Mozer, M.; Jordan, M.; Petsche, T., Advances in Neural Information Processing Systems 9 (1997), MIT Press), 176-182
[13] Efron, B.; Tibshirani, R. J., An Introduction to the Bootstrap (1993), Chapman and Hall · Zbl 0835.62038
[14] MacKay, D. J.C., A practical Bayesian framework for back-propagation networks, Neural Computation, 4, 3, 448-472 (1992)
[15] Neal, R. M., Bayesian Learning for Neural Networks, Lecture Notes in Statistics Series, No. 118 (1996), Springer
[16] Jang, J. S.R., ANFIS: Adaptive-network-based fuzzy inference systems, IEEE Trans. on System, Man and Cybernetics, 23, 3, 665-685 (1993)
[17] Neter, J.; Wasserman, W.; Kutner, M. H., Applied Linear Statistical Models: Regression, Analysis of Variance, and Experimental Designs (1985), Irwin
[18] Castellano, G.; Castiello, C.; Fanelli, A. M.; Mencar, C., Discovering prediction rules by a neuro-fuzzy modeling framework, (Palade, V.; Howlett, R. J.; Jain, L., Knowledge-Based Intelligent Information and Engineering Systems (KES 2003), Volume 1 (2003)), 1242-1248 · Zbl 1071.68535
[19] Castellano, G.; Castiello, C.; Fanelli, A. M.; Giovannini, M., A neuro-fuzzy framework for predicting ash properties in combustion processes, Neural, Parallel and Scientific Computation, 11, 69-82 (2003) · Zbl 1055.68551
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.