Proceedings ArticleDOI
Fuzzy systems are universal approximators
Li-Xin Wang
- pp 1163-1170
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TLDR
The Stone-Weierstrass theorem is used to prove that fuzzy systems with product inference, centroid defuzzification, and a Gaussian membership function are capable of approximating any real continuous function on a compact set to arbitrary accuracy.Abstract:
The author proves that fuzzy systems are universal approximators. The Stone-Weierstrass theorem is used to prove that fuzzy systems with product inference, centroid defuzzification, and a Gaussian membership function are capable of approximating any real continuous function on a compact set to arbitrary accuracy. This result can be viewed as an existence theorem of an optimal fuzzy system for a wide variety of problems. >read more
Citations
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Journal ArticleDOI
ANFIS: adaptive-network-based fuzzy inference system
TL;DR: The architecture and learning procedure underlying ANFIS (adaptive-network-based fuzzy inference system) is presented, which is a fuzzy inference System implemented in the framework of adaptive networks.
Journal ArticleDOI
Fuzzy basis functions, universal approximation, and orthogonal least-squares learning
Li-Xin Wang,Jerry M. Mendel +1 more
TL;DR: Using the Stone-Weierstrass theorem, it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy.
Journal ArticleDOI
Nonlinear black-box modeling in system identification: a unified overview
Jonas Sjöberg,Qinghua Zhang,Lennart Ljung,Albert Benveniste,Bernard Delyon,Pierre-Yves Glorennec,Håkan Hjalmarsson,Anatoli Juditsky +7 more
TL;DR: What are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system-identification application of these techniques are described, from a user's perspective.
Journal ArticleDOI
Fuzzy logic systems for engineering: a tutorial
TL;DR: After synthesizing a FLS, it is demonstrated that it can be expressed mathematically as a linear combination of fuzzy basis functions, and is a nonlinear universal function approximator, a property that it shares with feedforward neural networks.
Journal ArticleDOI
Stable adaptive fuzzy control of nonlinear systems
TL;DR: A direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control, is capable of incorporating fuzzy if-then control rules directly into the controllers, and guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded is developed.
References
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Journal ArticleDOI
Multilayer feedforward networks are universal approximators
TL;DR: It is rigorously established that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available.
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Multilayer feedforward networks are universal approximators
HornikK.,StinchcombeM.,WhiteH. +2 more
Journal ArticleDOI
Fuzzy logic in control systems: fuzzy logic controller. II
TL;DR: The basic aspects of the FLC (fuzzy logic controller) decision-making logic are examined and several issues, including the definitions of a fuzzy implication, compositional operators, the interpretations of the sentence connectives 'and' and 'also', and fuzzy inference mechanisms, are investigated.
Journal Article
Fuzzy logic in control systems : fuzzy logic controller. Part II
TL;DR: The fuzzy logic controller (FLC) based on fuzzy logic provides a means of converting a linguistic control strategy based on expert knowledge into an automatic control strategy.
Proceedings ArticleDOI
Back-propagation fuzzy system as nonlinear dynamic system identifiers
Li-Xin Wang,Jerry M. Mendel +1 more
TL;DR: The authors develop a training algorithm, similar to the backpropagation algorithm for neural networks, to train fuzzy systems to match desired input-output pairs and demonstrate how the fuzzy system learns to match an unknown nonlinear mapping as training progresses and that performance is improved by incorporating linguistic rules.