Multilayer feedforward networks are universal approximators
Neural Networks
Sufficient conditions on general fuzzy systems as function approximators
Automatica (Journal of IFAC)
Universal approximation by hierarchical fuzzy systems
Fuzzy Sets and Systems
Function approximation using fuzzy neural networks with robust learning algorithm
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Dynamic fuzzy neural networks-a novel approach to functionapproximation
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Modeling uncertainty in clinical diagnosis using fuzzy logic
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Approximation capabilities of hierarchical hybrid systems
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Approximation accuracy analysis of fuzzy systems as function approximators
IEEE Transactions on Fuzzy Systems
Analysis and design of hierarchical fuzzy systems
IEEE Transactions on Fuzzy Systems
Approximation Capabilities of Hierarchical Fuzzy Systems
IEEE Transactions on Fuzzy Systems
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Real-world systems usually involve both continuous and discrete input variables. However, in existing learning algorithms of both neural networks and fuzzy systems, these mixed variables are usually treated as continuous without taking into account the special features of discrete variables. It is inefficient to represent each discrete input variable having only a few fixed values by one input neuron with full connection to the hidden layer. This paper proposes a novel hierarchical hybrid fuzzy neural network to represent systems with mixed input variables. The proposed model consists of two levels: the lower level are fuzzy sub-systems each of which aggregates several discrete input variables into an intermediate variable as its output; the higher level is a neural network whose input variables consist of continuous input variables and intermediate variables. For systems or function approximations with mixed variables, it is shown that the proposed hierarchical hybrid fuzzy neural networks outperform standard neural networks in accuracy with fewer parameters, and both provide greater transparency and preserve the universal approximation property (i.e., they can approximate any function with mixed input variables to any degree of accuracy).