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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Book ChapterDOI
An attempt to employ genetic fuzzy systems to predict from a data stream of premises transactions
TL;DR: An approach to apply ensembles of genetic fuzzy systems, built over the chunks of a data stream, to aid in residential premises valuation was proposed and revealed its advantage in terms of predictive accuracy.
A Hybrid intelligent system for diagnosing and solving financial problems
TL;DR: A hybrid intelligent (neuro-fuzzy-symbolic) system is implemented to combine the inductive and deductive reasoning processes in a system to diagnose and indicate solutions to financial health problems of small and medium firms (SMF).
Book ChapterDOI
Support Vector Machines and Fuzzy Systems
TL;DR: This chapter presents a survey of the connection between fuzzy classifiers and kernel machines.
Journal ArticleDOI
Identification of the Hénon chaotic map by fuzzy modeling and Nelder–Mead simplex method
TL;DR: Numerical results indicate that the description of discrete chaotic dynamics of Henon map can be accomplished by exploring the effectiveness of NMO approach combined with T–S fuzzy modeling in constructing an appropriate nonlinear identification.
Fuzzy Miner: Extracting Fuzzy Rules from Numerical Patterns
TL;DR: In this article, a heuristic fuzzy method for the classification of numerical data is presented, followed by the design and the implementation of its corresponding tool (Fuzzy Miner), which is appropriately adjusted into pattern classification and an “adaptive†procedure is proposed for deriving highly accurate linguistic if-then rules.
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.