## Fuzzy Neural Network Theory and ApplicationThis book systematically synthesizes research achievements in the field of fuzzy neural networks in recent years. It also provides a comprehensive presentation of the developments in fuzzy neural networks, with regard to theory as well as their application to system modeling and image restoration. Special emphasis is placed on the fundamental concepts and architecture analysis of fuzzy neural networks. The book is unique in treating all kinds of fuzzy neural networks and their learning algorithms and universal approximations, and employing simulation examples which are carefully designed to help the reader grasp the underlying theory. This is a valuable reference for scientists and engineers working in mathematics, computer science, control or other fields related to information processing. It can also be used as a textbook for graduate courses in applied mathematics, computer science, automatic control and electrical engineering. Contents: Fuzzy Neural Networks for Storing and Classifying; Fuzzy Associative Memory OCo Feedback Networks; Regular Fuzzy Neural Networks; Polygonal Fuzzy Neural Networks; Approximation Analysis of Fuzzy Systems; Stochastic Fuzzy Systems and Approximations; Application of FNN to Image Restoration. Readership: Scientists, engineers and graduate students in applied mathematics, computer science, automatic control and information processing." |

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### Contents

Introduction 1 | 1 |

Fuzzy Neural Networks for Storing and Classifying 25 | 25 |

Fuzzy Associative MemoryFeedback Networks 68 | 68 |

Regular Fuzzy Neural Networks 131 | 131 |

Polygonal Fuzzy Neural Networks 199 | 199 |

Approximation Analysis of Fuzzy Systems 251 | 251 |

Stochastic Fuzzy Systems and Approximations 296 | 296 |

Application of FNN to Image Restoration 326 | 326 |

Indices 371 | 371 |

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antecedent fuzzy sets approximation capability arbitrary ARTx attractive basins attractor choose compact set connection weight matrix continuous function converges Corollary corresponding define defuzzification denazification denote error function FAM's fault-tolerance feedforward neural networks following fact holds fuzzy ART fuzzy inference networks fuzzy logic fuzzy matrix fuzzy neural networks fuzzy operators fuzzy pattern pair fuzzy rule fuzzy sets fuzzy valued functions fuzzy weights gray levels Hongxing Hopfield networks I/O relationship IEEE IEEE Trans imply impulse noise inference rules input patterns Internat Ishibuchi learning algorithm Lemma Liu Puyin Mamdani fuzzy system Moreover neuro-fuzzy neuron node obtain output parameters pattern pair family polygonal FNN's Proc Proof regular FNN's regular fuzzy respectively Sets and Systems shown in Figure Similarly stochastic process Suppose T-S fuzzy system Theorem trapezoidal fuzzy numbers universal approximation vector