Learning internal representations by error propagation
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1
Kolmogorov's theorem and multilayer neural networks
Neural Networks
Neural network design
Bounds for the Computational Power and Learning Complexity of Analog Neural Nets
SIAM Journal on Computing
Extraction of Logical Rules from Neural Networks
Neural Processing Letters
Rule-extraction by backpropagation of polyhedra
Neural Networks
Rule extraction by successive regularization
Neural Networks
On the complexity of recognizing regions computable by two-layered perceptrons
Annals of Mathematics and Artificial Intelligence
Observational Logic Integrates Data Mining Based on Statistics and Neural Networks
PKDD '00 Proceedings of the 4th European Conference on Principles of Data Mining and Knowledge Discovery
Weierstrass Approximations by Łukasiewicz Formulas with One Quantified Variable
ISMVL '01 Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Knowledge-based fuzzy MLP for classification and rule generation
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Extracting rules from trained neural networks
IEEE Transactions on Neural Networks
Neuro-fuzzy rule generation: survey in soft computing framework
IEEE Transactions on Neural Networks
A new methodology of extraction, optimization and application of crisp and fuzzy logical rules
IEEE Transactions on Neural Networks
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The extraction of logical rules from data by means of artificial neural networks is receiving increasingly much attention. The meaning the extracted rules may convey is primarily determined by the set of their possible truth values, according to which two basic kinds of rules can be differentiated - Boolean and fuzzy. Though a wide spectrum of theoretical principles has been proposed for ANN-based rule extraction, most of the existing methods still rely mainly on heuristics. Moreover, so far apparently no particular principles have been employed for the extraction of both kinds of rules, what can be a serious drawback when switching between Boolean and fuzzy rules. This paper presents a mathematically well founded approach based on piecewise-linear activation functions, which is suitable for the extraction of both kinds of rules. Basic properties of piecewise-linear neural networks are reviewed, most importantly, the replaceability of suboptimal computable mappings, and the preservation of polyhedra. Based on those results, a complete algorithm for the extraction of Boolean rules with that approach is given. In addition, two modifications of the algorithm are described, relying on different assumptions about the way how the properties of a polyhedron determine the decision to replace the polyhedron with a hyperrectangle. Finally, a biological application in which the presented approach has been successfully employed is briefly sketched.