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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An incremental construction learning algorithm for identification of T-S Fuzzy Systems
TL;DR: An incremental construction learning algorithm for identification of T-S fuzzy Systems that can automatically determines and controls the number and location of fuzzy terms needed by following the error-reducing driven evolving process to achieve the desired accuracy.
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The Fuzzy Systems Handbook: A Practitioner’s Guide to Building, Using, and Maintaining Fuzzy Systems (Earl Cox)
TL;DR: The Fuzzy Systems Handbook is a practitioner’s guide to fuzzy logic: alpha-level sets, fuzzy quantifiers and hedges, set intersection and union, compensatory set operators, and the compositional rules of inference.
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Fuzzy systems with overlapping Gaussian concepts: approximation properties in Sobolev norms
TL;DR: A new method for the computation of the system coefficients is provided, showing that it guarantees uniform approximation of the derivatives of the target function.
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AI Therapist Realizing Expert Verbal Cues for Effective Robot-Assisted Gait Training
TL;DR: An AI therapist (AI-T) is proposed that implements the verbal cues of professional therapists having extensive experience with robot-assisted gait training using the SUBAR for stroke patients using a neuro-fuzzy system.
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Active Shimmy Damping Using Direct Adaptive Fuzzy Control
TL;DR: In this article, a new active damping controller was developed in the context of the European DRESS (Distributed and Redundant Electro-mechanical nose gear Steering System) project for avoiding the shimmy oscillation.
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.