Journal ArticleDOI
Fuzzy systems as universal approximators
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An additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy.Abstract:
An additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. An additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input-output state space and averaging patches that overlap. The fuzzy system computes a conditional expectation E|Y|X| if we view the fuzzy sets as random sets. Each fuzzy rule defines a fuzzy patch and connects commonsense knowledge with state-space geometry. Neural or statistical clustering systems can approximate the unknown fuzzy patches from training data. These adaptive fuzzy systems approximate a function at two levels. At the local level the neural system approximates and tunes the fuzzy rules. At the global level the rules or patches approximate the function. >read more
Citations
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Data driven modeling based on dynamic parsimonious fuzzy neural network
TL;DR: DPFNN is a four layers network, which features coalescence between TSK (Takagi-Sugeno-Kang) fuzzy architecture and multivariate Gaussian kernels as membership functions, and delivers more compact and parsimonious network structures.
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Global stability of generalized additive fuzzy systems
TL;DR: The paper explores the stability of a class of feedback fuzzy systems that compute a system output as a convex sum of linear operators and derives the basic ratio structure of additive fuzzy systems and shows how supervised learning can tune their parameters.
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Fuzzy Systems Are Universal Approximators for a Smooth Function and Its Derivatives
TL;DR: It is shown that for any given accuracy, fuzzy systems can approximate an arbitrary smooth function by a fuzzy system so that not only the function is approximated within this accuracy, but its derivatives are approximated as well.
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Fuzzy logic rotor position estimation based switched reluctance motor DSP drive with accuracy enhancement
TL;DR: This paper describes a novel angle estimation scheme for a real time digital signal processor (DSP) based switched reluctance motor drive using fuzzy logic where several unique techniques are implemented to improve the estimation accuracy.
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Data-Based Virtual Unmodeled Dynamics Driven Multivariable Nonlinear Adaptive Switching Control
TL;DR: The concepts of controller-driven model and virtual unmodeled dynamics to propose a new design framework are explored and simulation and experimental tests on a heavily coupled nonlinear twin-tank system are carried out to confirm the effectiveness of the proposed method.
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.
Journal ArticleDOI
Multilayer feedforward networks are universal approximators
HornikK.,StinchcombeM.,WhiteH. +2 more
Book
Fuzzy Sets and Systems: Theory and Applications
Didier Dubois,Henri Prade +1 more
TL;DR: This book effectively constitutes a detailed annotated bibliography in quasitextbook style of the some thousand contributions deemed by Messrs. Dubois and Prade to belong to the area of fuzzy set theory and its applications or interactions in a wide spectrum of scientific disciplines.
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.