## Abstract

This chapter describes the development of a hybrid learning

procedure for a typical Fuzzy-Neural Network. In the classical case, the

learning of such kind of networks is being performed by the application of

the Gradient Descent. Due to its disadvantages to stuck in a local minima

and a slower convergence rate, implies the development of new learning

approaches in order to enable the possibility to be modeled more complex

dynamics. An alternative to be used is the second order gradient

approaches, based on Newton-like methods, since they provide a more

faster and efficient parameter learning. In the fuzzy-neural networks architectures has to be identified at each sampling period two groups of

parameters: the premise - the parameters of the fuzzy membership functions

and the consequent - the coefficients into the fuzzy rules. Since,

the first group of parameters is sensitive to application of faster learning

approaches, which may lead to model oscillations, a natural choice is to

develop a hybrid approach. It is proposed a two step learning algorithm,

based on minimization of an instant error function, which adjust the

fuzzy rule premise parameters by a Gradient descent approach, while the

rule consequents are scheduled either by Gauss-Newton and Levenberg-

Marquardt approaches. The efficency of the proposed approach is studied

through prediction by the proposed Fuzzy-Neural Network of two

common Chaotic Time Series: Rossler and Mackey-Glass.

procedure for a typical Fuzzy-Neural Network. In the classical case, the

learning of such kind of networks is being performed by the application of

the Gradient Descent. Due to its disadvantages to stuck in a local minima

and a slower convergence rate, implies the development of new learning

approaches in order to enable the possibility to be modeled more complex

dynamics. An alternative to be used is the second order gradient

approaches, based on Newton-like methods, since they provide a more

faster and efficient parameter learning. In the fuzzy-neural networks architectures has to be identified at each sampling period two groups of

parameters: the premise - the parameters of the fuzzy membership functions

and the consequent - the coefficients into the fuzzy rules. Since,

the first group of parameters is sensitive to application of faster learning

approaches, which may lead to model oscillations, a natural choice is to

develop a hybrid approach. It is proposed a two step learning algorithm,

based on minimization of an instant error function, which adjust the

fuzzy rule premise parameters by a Gradient descent approach, while the

rule consequents are scheduled either by Gauss-Newton and Levenberg-

Marquardt approaches. The efficency of the proposed approach is studied

through prediction by the proposed Fuzzy-Neural Network of two

common Chaotic Time Series: Rossler and Mackey-Glass.

Original language | English |
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Title of host publication | Mathematics in Industry |

Editors | Angela Slavova |

Pages | 246-257 |

Number of pages | 12 |

ISBN (Electronic) | (13): 978-1-4438-6401-5 |

Publication status | Published - 2013 |

MoE publication type | A3 Part of a book or another research book |

## Keywords

- Fuzzy-neural networks
- neural network modeling
- neural network systems