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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Journal ArticleDOI
Bayesian Inference With Adaptive Fuzzy Priors and Likelihoods
TL;DR: A uniform approximation theorem for Bayesian posteriors is proved: An additive fuzzy posterior uniformly approximates the posterior probability density if the prior or likelihood densities are continuous and bounded and if separate additive fuzzy systems approximate the prior and likelihood density.
Dissertation
Fuzzy-Wavelet Method for Time Series Analysis
TL;DR: An investigation of the effectiveness of subtractive clustering fuzzy models in analyzing time series that are deemed to have trend and seasonal components indicates that, in general, forecast performance improves when pre-processed data is used.
Proceedings ArticleDOI
Takagi-Sugeno models as approximators in Sobolev norms: the SISO case
TL;DR: Classical results on the approximation of regular functions are improved showing that these more general models may approximate to any degree of accuracy not only sufficiently smooth functions but also their first and second-order derivatives.
Journal ArticleDOI
An adaptive fuzzy controller based on harmony search and its application to power plant control
TL;DR: In this article, a novel adaptive fuzzy controller is presented to implement non-overshoot control in power plants in which the Lyapunov-based adaptive law is employed to guarantee the stability of the controller while a modified Adaptive Binary Harmony Search (ABHS) algorithm is utilized to search the optimal control parameters to improve the dynamic performance.
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.