Data processing: artificial intelligence – Fuzzy logic hardware – Fuzzy neural network
Reexamination Certificate
1998-11-23
2001-11-13
Davis, George B. (Department: 2122)
Data processing: artificial intelligence
Fuzzy logic hardware
Fuzzy neural network
Reexamination Certificate
active
06317730
ABSTRACT:
BACKGROUND OF THE INVENTION
In the prediction of time series, or also in the modeling of processes with the aid of neural networks, expert knowledge is often ignored. Since, however, in many cases experts can be found for the respective problematic who are in a position to express their knowledge in the form of fuzzy rules, what are called neuro-fuzzy systems are used for predicting time series or for modeling processes, whereby fuzzy systems and neural networks, with their respective characteristic properties, are combined with one another.
A fuzzy system specified by means of rules is thereby standardly translated into a neural network equivalent to the rules, and the neural network is optimized on the basis of training data. The optimized neural network is then again mapped onto fuzzy rules, whereby knowledge concerning the now-optimized system is extractable for an expert. This would not be possible given the exclusive use of neural networks.
Basic principles of neuro-fuzzy systems are known for example from document, R. Kruse et al., Neuronale Fuzzy-Systeme, Spektrum der Wissenschaft, S. 34-41, June 1995.
An overview of various learning methods for neural networks, for example monitored learning methods or unmonitored learning methods, are known from document, J. Hertz et al., Introduction to the Theory of Neural Computation, Lecture Notes Volume I, Addison Wesley Publishing Company, ISBN 0-201-51560-1, 1995.
Methods for removing (pruning) or, respectively, reviving (growing) weights and/or neurons of a neural network are known for example from document, C. Bishop, Neuronal Networks for Pattern Recognition, Clarendon Press, Oxford, ISBN 0-198-538-642, pp.353-364, 1995 and document, A. Gail et al., Rule Extraction: From Neural Architecture to Symbolic Representation, Connection Science, vol. 7, no.1, pp. 3-27, 1995.
In addition, it is known from document, R. Neuneier and H. G. Zimmermann, A Semantic-Preserving Learning Algorithm for Neuro-Fuzzy Systems with Applications to Time Series Prediction, Proceedings of the ICANN Workshop “Banking, Finance and Insurance,” Paris, pp. 1-5, 1995, to use semantics-preserving learning algorithms for the training of the neural network of a neuro-fuzzy system, so that the new rules of the fuzzy rule set continue to make correct and useful statements.
In addition, it is also known from document, R. Neuneier and H. G. Zimmermann, A Semantic-Preserving Learning Algorithm for Neuro-Fuzzy Systems with Applications to Time Series Prediction, Proceedings of the ICANN Workshop “Banking, Finance and Insurance,” Paris, pp.1-5, 1995, to prune entire rules of the rule set in the optimization of the neural network of a neuro-fuzzy system.
In addition, what is called an early-stopping method is also known from document, W. Finnoff et al., Improving Generalization by Nonconvergent Model Selection Methods, Neural Networks, no. 6, 1992, for the pruning or, respectively, growth of the weights and/or neurons of a neural network.
In the document, H. Hensel et al., Optimierung von Fuzzy-Control mit Hilfe Neuronaler Netze, atp, Automatisierungstechnische Praxis, vol. 37, no. 11, pp. 40-48, 1995, an overview concerning the optimization of fuzzy control with the aid of neural networks is specified.
From, J. Hollatz, Integration von regelbasiertem Wissen in neuronale Netze, Dissertation Institut für Informatik, Technische Universität München, pp. 35-58, 1993, an overview is known concerning the design of rules and the transformation of rules in neural networks.
The pruning of entire rules in a fuzzy rule set has the disadvantage that the granularity of the optimization of the fuzzy rule set is very rough. For this reason, the precision of the fuzzy rule set obtained is relatively low. The results achieved with the optimized fuzzy rule set are also imprecise with this known method.
SUMMARY OF THE INVENTION
The invention is thus based on the problem of indicating a method for optimizing a fuzzy rule set that yields a more powerful, better optimized fuzzy rule set than is possible with the known method.
In general terms the present invention is a method for optimizing a predetermined fuzzy rule set having an arbitrary number of rules using a computer. The fuzzy rule set is mapped onto a neuronal network. A respective neuron of the neural network describes a rule of the fuzzy rule set. A respective weight of a neuron describes a premise of the rule that is described by the corresponding neuron. The neural network is trained. the new neural network is mapped onto a new fuzzy rule set, whereby the new fuzzy rule set is characterized by the new neural network. Individual weights of the neural network are pruned or grown, whereby a new neural network is formed, in which individual premises of the rules of the fuzzy rule set are pruned or, respectively, added.
Advantageous developments of the present invention are as follows.
An error is determined for the new neural network. For the case in which the error lies under a predeterminable limit, the method is terminated and the new fuzzy rule set represents the optimal fuzzy rule set. For the case in which the error lies above the limit, the method is repeated iteratively until the error lies below the limit. The premises of the rules are described with the weights of the neural network. The premises of the rules are coded in binary fashion with the weights of the neural network.
A gradient decrease method is used for the training of the neural network.
A semantics-preserving learning algorithm is used for the training of the neural network.
Rules of the new fuzzy rule set with identical semantics are combined to form a new rule. A reliability value of the new rule results from the sum of the reliability values of the rules that are combined to form the new rule.
Activation functions of neurons of the neural network respectively correspond to a rule.
In this method, carried out using a computer, a fuzzy rule set is mapped onto a neural network. The neural network is trained, and subsequently weights and/or neurons of the trained neural network are pruned and/or grown for the trained neural network. In a last step, a new neural network formed in this way is mapped onto a new fuzzy rule set.
By taking into account individual weights and/or neurons in the pruning or, respectively, growth in the neural network, a higher granularity is achieved in the modification of the individual rules of the fuzzy rule set by means of the pruning or, respectively, growth of elements of the neural network. The granularity is increased in such a way that not only are entire rules pruned from the fuzzy rule set, but rather individual premises of the rules of the fuzzy rule set can be pruned or, respectively, added. By this means, the power and reliability, and thus the achieved results of the neuro-fuzzy system, are increased considerably.
It is advantageous to carry out the method iteratively until an error determined for the respective current neural network lies under a predeterminable threshold. In this way it is possible on the one hand to form an evaluation of the respectively formed neural network and of the new fuzzy rule set determined therefrom, and on the other hand to control the “quality” of the respective new fuzzy rule set in such a way that it achieves a predeterminable quality.
In addition, it is advantageous to construct the structure of the neural network in such a way that the premises of the rules are described with the weights of the neural network. By this means, the pruning or, respectively, the growth of premises of the rules is already enabled by pruning or, respectively, growth of the weights of the neural network. A further simplification in the optimization of the fuzzy rule set is achieved in that the premises of the rules are coded in binary fashion with the weights of the neural network. In this way, a very simple optimization of the rule set is possible that is easily surveyable for the optimization of the fuzzy rule set and is connected with a low computing expense.
In order further to increase the reliability o
Neuneier Ralf
Siekmann Stefan
Zimmermann Hans-Georg
Davis George B.
Schiff & Hardin & Waite
Siemens Aktiengesellschaft
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