Communications of the ACM
Induction of finite-state languages using second-order recurrent networks
Neural Computation
Learning finite machines with self-clustering recurrent networks
Neural Computation
Extraction of rules from discrete-time recurrent neural networks
Neural Networks
Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence
Neuro-fuzzy and soft computing: a computational approach to learning and machine intelligence
Knowledge-based neurocomputing
Knowledge-based neurocomputing
Knowledge-based neurocomputing
Structural learning and rule discovery
Knowledge-based neurocomputing
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Recurrent Neural Networks: Design and Applications
Recurrent Neural Networks: Design and Applications
What Inductive Bias Gives Good Neural Network Training Performance?
IJCNN '00 Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks (IJCNN'00)-Volume 3 - Volume 3
Rule Extraction from Recurrent Neural Networks: A Taxonomy and Review
Neural Computation
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
Introduction to Automata Theory, Languages, and Computation (3rd Edition)
A learning algorithm for continually running fully recurrent neural networks
Neural Computation
A study of cross-validation and bootstrap for accuracy estimation and model selection
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Some studies in machine learning using the game of checkers
IBM Journal of Research and Development
Are fuzzy sets a reasonable tool for modeling vague phenomena?
Fuzzy Sets and Systems
On generating FC3 fuzzy rule systems from data usingevolution strategies
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Hyperbolic optimal control and fuzzy control
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Fuzzy logic = computing with words
IEEE Transactions on Fuzzy Systems
Fuzzy finite-state automata can be deterministically encoded into recurrent neural networks
IEEE Transactions on Fuzzy Systems
Designing fuzzy inference systems from data: An interpretability-oriented review
IEEE Transactions on Fuzzy Systems
Fuzzy-set based models of neurons and knowledge-based networks
IEEE Transactions on Fuzzy Systems
Learning capacity and sample complexity on expert networks
IEEE Transactions on Neural Networks
A new recurrent neural-network architecture for visual pattern recognition
IEEE Transactions on Neural Networks
Are artificial neural networks black boxes?
IEEE Transactions on Neural Networks
Inductive inference from noisy examples using the hybrid finite state filter
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Neuro-fuzzy rule generation: survey in soft computing framework
IEEE Transactions on Neural Networks
Interpretation of artificial neural networks by means of fuzzy rules
IEEE Transactions on Neural Networks
Are artificial neural networks white boxes?
IEEE Transactions on Neural Networks
Multilayer perceptron, fuzzy sets, and classification
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
A New Approach to Knowledge-Based Design of Recurrent Neural Networks
IEEE Transactions on Neural Networks
Functional equivalence between radial basis function networks and fuzzy inference systems
IEEE Transactions on Neural Networks
An evolutionary algorithm that constructs recurrent neural networks
IEEE Transactions on Neural Networks
Fuzzy multi-layer perceptron, inferencing and rule generation
IEEE Transactions on Neural Networks
Analysis of artificial neural network learning near temporary minima: A fuzzy logic approach
Fuzzy Sets and Systems
Equivalences between neural-autoregressive time series models and fuzzy systems
IEEE Transactions on Neural Networks
An expert fuzzy cognitive map for reactive navigation of mobile robots
Fuzzy Sets and Systems
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Considerable research has been devoted to the integration of fuzzy logic (FL) tools with classic artificial intelligence (AI) paradigms. One reason for this is that FL provides powerful mechanisms for handling and processing symbolic information stated using natural language. In this respect, fuzzy rule-based systems are white-boxes, as they process information in a form that is easy to understand, verify and, if necessary, refine. The synergy between artificial neural networks (ANNs), which are notorious for their black-box character, and FL proved to be particularly successful. Such a synergy allows combining the powerful learning-from-examples capability of ANNs with the high-level symbolic information processing of FL systems. In this paper, we present a new approach for extracting symbolic information from recurrent neural networks (RNNs). The approach is based on the mathematical equivalence between a specific fuzzy rule-base and functions composed of sums of sigmoids. We show that this equivalence can be used to provide a comprehensible explanation of the RNN functioning. We demonstrate the applicability of our approach by using it to extract the knowledge embedded within an RNN trained to recognize a formal language.