Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification
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 ef...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2013/136214 |
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| author | Oscar Castillo Juan R. Castro Patricia Melin Antonio Rodriguez-Diaz |
| author_facet | Oscar Castillo Juan R. Castro Patricia Melin Antonio Rodriguez-Diaz |
| author_sort | Oscar Castillo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b7938d5bf4f14dfea31aa4af5a076ead |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-b7938d5bf4f14dfea31aa4af5a076ead2025-02-03T05:59:08ZengWileyAdvances in Fuzzy Systems1687-71011687-711X2013-01-01201310.1155/2013/136214136214Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear IdentificationOscar Castillo0Juan R. Castro1Patricia Melin2Antonio Rodriguez-Diaz3Tijuana Institute of Technology, 22379 Tijuana, BCN, MexicoBaja California Autonomous University (UABC), 22379 Tijuana, BCN, MexicoTijuana Institute of Technology, 22379 Tijuana, BCN, MexicoBaja California Autonomous University (UABC), 22379 Tijuana, BCN, MexicoNeural 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.http://dx.doi.org/10.1155/2013/136214 |
| spellingShingle | Oscar Castillo Juan R. Castro Patricia Melin Antonio Rodriguez-Diaz Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification Advances in Fuzzy Systems |
| title | Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification |
| title_full | Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification |
| title_fullStr | Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification |
| title_full_unstemmed | Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification |
| title_short | Universal Approximation of a Class of Interval Type-2 Fuzzy Neural Networks in Nonlinear Identification |
| title_sort | universal approximation of a class of interval type 2 fuzzy neural networks in nonlinear identification |
| url | http://dx.doi.org/10.1155/2013/136214 |
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