On the Universal Approximation Theorem of Fuzzy Neural Networks with Random Membership Function Parameters

2005 ◽  
pp. 45-50 ◽  
Author(s):  
Lipo Wang ◽  
Bing Liu ◽  
Chunru Wan
Keyword(s):  
Neural Networks ◽  
Membership Function ◽  
Approximation Theorem ◽  
Fuzzy Neural Networks ◽  
Universal Approximation ◽  
Fuzzy Neural

scholarly journals Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Oscar Castillo ◽  
Juan R. Castro ◽  
Patricia Melin ◽  
Antonio Rodriguez-Diaz
Keyword(s):  
Neural Networks ◽  
Fuzzy Logic ◽  
Nonlinear Function ◽  
Fuzzy Neural Networks ◽  
Universal Approximation ◽  
Fuzzy Logic Systems ◽  
Fuzzy Neural ◽  
Logic Systems ◽  
Interval Type

Neural networks (NNs), type-1 fuzzy logic systems (T1FLSs), and interval type-2 fuzzy logic systems (IT2FLSs) have been shown to be universal approximators, which means that they can approximate any nonlinear continuous function. Recent research shows that embedding an IT2FLS on an NN can be very effective for a wide number of nonlinear complex systems, especially when handling imperfect or incomplete information. In this paper we show, 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 interval type-2 membership functions (IT2MFs) for this purpose. Simulation results of nonlinear function identification using the IT2FNN for one and three variables and for the Mackey-Glass chaotic time series prediction are presented to illustrate the concept of universal approximation.

Modeling of Self-Induced Vibrations that Occur During the Machining Process of Casting Patterns with the Use of The Fuzzy-Neural Networks Method

2013 ◽  
Vol 58 (3) ◽  
pp. 871-875
Author(s):  
A. Herberg
Keyword(s):  
Neural Networks ◽  
Control System ◽  
Network Structure ◽  
Fuzzy Systems ◽  
Fuzzy Neural Networks ◽  
Cnc Machining ◽  
Machining Process ◽  
Modeling Process ◽  
Fuzzy Neural ◽  
Takagi Sugeno

Abstract This article outlines a methodology of modeling self-induced vibrations that occur in the course of machining of metal objects, i.e. when shaping casting patterns on CNC machining centers. The modeling process presented here is based on an algorithm that makes use of local model fuzzy-neural networks. The algorithm falls back on the advantages of fuzzy systems with Takagi-Sugeno-Kanga (TSK) consequences and neural networks with auxiliary modules that help optimize and shorten the time needed to identify the best possible network structure. The modeling of self-induced vibrations allows analyzing how the vibrations come into being. This in turn makes it possible to develop effective ways of eliminating these vibrations and, ultimately, designing a practical control system that would dispose of the vibrations altogether.

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