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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Proceedings ArticleDOI
The representation problem for additive fuzzy systems
TL;DR: It is proved that all bounded scalar functions of one variable have a fuzzy representation and that functions of two or more variables need not and that use of bipolar membership functions can expand the domain of definition for a representation without increasing computational load.
Journal ArticleDOI
Additive Fuzzy Systems: From Generalized Mixtures to Rule Continua
TL;DR: A separation theorem shows how fuzzy approximators combine with exact Watkins‐based two‐rule function representations in a higher‐level convex sum of the combined systems.
Journal ArticleDOI
Hierarchical Fuzzy Systems for Function Approximation on Discrete Input Spaces With Application
TL;DR: It is proven that any function on a discrete space can be approximated to any degree of accuracy by hierarchical fuzzy systems with any desired separable hierarchical structure and a discrete version of Kolmogorov's theorem is obtained.
Journal ArticleDOI
Universal approximation of a class of interval type-2 fuzzy neural networks in nonlinear identification
TL;DR: This paper shows, 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 intervaltype-2membership functions ( IT2MFs) for this purpose.
Proceedings ArticleDOI
A parallel tabu search based fuzzy inference method for short-term load forecasting
TL;DR: Parallel tabu search is used to globally optimize the number and location of the fuzzy membership functions and considers two strategies of the neighborhood decomposition and multiple tabu lengths so that computational efficiency and solution accuracy are improved.
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.