Fuzzy nonlinear regression with fuzzified radial basis function network

A fuzzified radial basis function network (FRBFN) is a kind of fuzzy neural network that is obtained by direct fuzzification of the well known neural model RBFN. A FRBFN contains fuzzy weights and can handle fuzzy-in fuzzy-out data. This paper shows that a FRBFN can also be interpreted as a kind of...

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Published in:IEEE transactions on fuzzy systems Vol. 13; no. 6; pp. 742 - 760
Main Authors: Dong Zhang, Luo-Feng Deng, Kai-Yuan Cai, So, A.
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2005
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Fuzzified radial basis function network (FRBFN)
Fuzzy logic
fuzzy neural network
Fuzzy neural networks
fuzzy number
fuzzy regression
Fuzzy sets
Hybrid intelligent systems
Mathematical programming
Measurement errors
Multidimensional systems
Neural networks
Radial basis function networks
Regression analysis
Statistical analysis
Studies
universal approximation
ISSN:1063-6706, 1941-0034
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Abstract A fuzzified radial basis function network (FRBFN) is a kind of fuzzy neural network that is obtained by direct fuzzification of the well known neural model RBFN. A FRBFN contains fuzzy weights and can handle fuzzy-in fuzzy-out data. This paper shows that a FRBFN can also be interpreted as a kind of fuzzy expert system. Hence it owns the advantages of simple structure and clear physical meaning. Some metrics for fuzzy numbers have been extended to the metrics for n-dimensional fuzzy vectors, which are applicable to computations in FRBFNs. The corresponding metric spaces for n-dimensional fuzzy vectors are proved to be complete. Further, FRBFNs are proved to be able to act as universal function approximators for any continuous fuzzy function defined on a compact set. This paper applies the proposed FRBFN to nonparametric fuzzy nonlinear regression problems for multidimensional LR-type fuzzy data. Fuzzy nonlinear regression with FRBFNs can be formulated as a nonlinear mathematical programming problem. Two training algorithms are proposed to quickly solve the two types of problems under different criteria and constraint conditions, namely, the two-stage and BP (Back-Propagation) training algorithms. Simulation studies are carried out to verify the feasibility and demonstrate the advantages of the proposed approaches.
AbstractList [...] it owns the advantages of simple structure and clear physical meaning.
A fuzzified radial basis function network (FRBFN) is a kind of fuzzy neural network that is obtained by direct fuzzification of the well known neural model RBFN. A FRBFN contains fuzzy weights and can handle fuzzy-in fuzzy-out data. This paper shows that a FRBFN can also be interpreted as a kind of fuzzy expert system. Hence it owns the advantages of simple structure and clear physical meaning. Some metrics for fuzzy numbers have been extended to the metrics for n-dimensional fuzzy vectors, which are applicable to computations in FRBFNs. The corresponding metric spaces for n-dimensional fuzzy vectors are proved to be complete. Further, FRBFNs are proved to be able to act as universal function approximators for any continuous fuzzy function defined on a compact set. This paper applies the proposed FRBFN to nonparametric fuzzy nonlinear regression problems for multidimensional LR-type fuzzy data. Fuzzy nonlinear regression with FRBFNs can be formulated as a nonlinear mathematical programming problem. Two training algorithms are proposed to quickly solve the two types of problems under different criteria and constraint conditions, namely, the two-stage and BP (Back-Propagation) training algorithms. Simulation studies are carried out to verify the feasibility and demonstrate the advantages of the proposed approaches.
Author Dong Zhang
Kai-Yuan Cai
Luo-Feng Deng
So, A.
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Snippet A fuzzified radial basis function network (FRBFN) is a kind of fuzzy neural network that is obtained by direct fuzzification of the well known neural model...
[...] it owns the advantages of simple structure and clear physical meaning.
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SubjectTerms Algorithms
Fuzzified radial basis function network (FRBFN)
Fuzzy logic
fuzzy neural network
Fuzzy neural networks
fuzzy number
fuzzy regression
Fuzzy sets
Hybrid intelligent systems
Mathematical programming
Measurement errors
Multidimensional systems
Neural networks
Radial basis function networks
Regression analysis
Statistical analysis
Studies
universal approximation
Title Fuzzy nonlinear regression with fuzzified radial basis function network
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