Open AccessUniversal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification
Author(s) -
Oscar Castillo,
Juan R. Castro,
Patricia Melín,
Antonio Rodríguez-Díaz
Publication year - 2013
Publication title -
advances in fuzzy systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.38
H-Index - 19
eISSN - 1687-711X
pISSN - 1687-7101
DOI - 10.1155/2013/136214
Subject(s) - interval (graph theory) , artificial neural network , chaotic , nonlinear system , fuzzy logic , type (biology) , mathematics , class (philosophy) , computer science , fuzzy set , embedding , membership function , artificial intelligence , ecology , physics , quantum mechanics , combinatorics , biology
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
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