Multilayer feedforward networks are universal approximators
Neural Networks
Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence
Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence
Automatica (Journal of IFAC)
Sugeno type controllers are universal controllers
Fuzzy Sets and Systems
Can fuzzy neural nets approximate continuous fuzzy functions?
Fuzzy Sets and Systems
Fuzzy Systems as Universal Approximators
IEEE Transactions on Computers
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
Universal approximation by hierarchical fuzzy system with constraints on the fuzzy rule
Fuzzy Sets and Systems - Fuzzy models
Pattern Recognition, Third Edition
Pattern Recognition, Third Edition
Hybrid Learning Algorithm for Interval Type-2 Fuzzy Neural Networks
GRC '07 Proceedings of the 2007 IEEE International Conference on Granular Computing
A hybrid learning algorithm for a class of interval type-2 fuzzy neural networks
Information Sciences: an International Journal
On constructing parsimonious type-2 fuzzy logic systems via influential rule selection
IEEE Transactions on Fuzzy Systems
Fuzzy subsethood for fuzzy sets of type-2 and generalized type-n
IEEE Transactions on Fuzzy Systems
Dynamical optimal training for interval type-2 fuzzy neural network (T2FNN)
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Interval type-2 fuzzy logic systems: theory and design
IEEE Transactions on Fuzzy Systems
OR/AND neuron in modeling fuzzy set connectives
IEEE Transactions on Fuzzy Systems
Fuzzy basis functions, universal approximation, and orthogonal least-squares learning
IEEE Transactions on Neural Networks
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Neural networks (NNs), type-1 fuzzy logic systems (T1FLSs), and interval type-2 fuzzy logic systems (IT2FLSs) have been shown to be universal approximators, which means that they can approximate any nonlinear continuous function. Recent research shows that embedding an IT2FLS on an NN can be very effective for a wide number of nonlinear complex systems, especially when handling imperfect or incomplete information. In this paper we show, based on the Stone-Weierstrass theorem, that an interval type-2 fuzzy neural network (IT2FNN) is a universal approximator, which uses a set of rules and interval type-2membership functions (IT2MFs) for this purpose. Simulation results of nonlinear function identification using the IT2FNN for one and three variables and for the Mackey-Glass chaotic time series prediction are presented to illustrate the concept of universal approximation.