Learning internal representations by error propagation
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1
Approximation capabilities of multilayer feedforward networks
Neural Networks
Kolmogorov's theorem and multilayer neural networks
Neural Networks
C4.5: programs for machine learning
C4.5: programs for machine learning
Extracting Refined Rules from Knowledge-Based Neural Networks
Machine Learning
A constructive proof of McNaughton's theorem in infinite-valued logic
Journal of Symbolic Logic
Neural network design
Bounds for the Computational Power and Learning Complexity of Analog Neural Nets
SIAM Journal on Computing
Extracting rules from neural networks by pruning and hidden-unit splitting
Neural Computation
Extraction of Logical Rules from Neural Networks
Neural Processing Letters
Template-based procedures for neural network interpretation
Neural Networks
Multivariate data analysis and modeling through classification and regression trees
Computational Statistics & Data Analysis
Rule-extraction by backpropagation of polyhedra
Neural Networks
A new algorithm for learning in piecewise-linear neural networks
Neural Networks
Some consequences of Herbrand and McNaughton theorems in fuzzy logic
Discovering the world with fuzzy logic
Symbolic knowledge extraction from trained neural networks: a sound approach
Artificial Intelligence
Rule extraction by successive regularization
Neural Networks
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Pattern Recognition and Neural Networks
Pattern Recognition and Neural Networks
Intelligent Data Analysis: An Introduction
Intelligent Data Analysis: An Introduction
Effective Data Mining Using Neural Networks
IEEE Transactions on Knowledge and Data Engineering
Symbolic Rule Extraction from the DIMLP Neural Network
Hybrid Neural Systems, revised papers from a workshop
Extraction of Logical Rules from Data by Means of Piecewise-Linear Neural Networks
DS '02 Proceedings of the 5th International Conference on Discovery Science
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)
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Acquiring rule sets as a product of learning in a logical neural architecture
IEEE Transactions on Neural Networks
Are artificial neural networks black boxes?
IEEE Transactions on Neural Networks
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
Measures of Ruleset Quality Capable to Represent Uncertain Validity
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Measures of ruleset quality for general rules extraction methods
International Journal of Approximate Reasoning
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This article addresses the topic of extracting logical rules from data by means of artificial neural networks. The approach based on piecewise linear neural networks is revisited, which has already been used for the extraction of Boolean rules in the past, and it is shown that this approach can be important also for the extraction of fuzzy rules. Two important theoretical properties of piecewise-linear neural networks are proved, allowing an elaboration of the basic ideas of the approach into several variants of an algorithm for the extraction of Boolean rules. That algorithm has already been used in two real-world applications. Finally, a connection to the extraction of rules of the Łukasiewicz logic is established, relying on recent results about rational McNaughton functions. Based on one of the constructive proofs of the McNaughton theorem, an algorithm is formulated that in principle allows extracting a particular kind of formulas of the Łukasiewicz predicate logic from piecewise-linear neural networks trained with rational data.