Fuzzy neural intelligent systems : mathematical foundation and the applications in engineering

Abstract

FOUNDATION OF FUZZY SYSTEMS Definition of Fuzzy Sets Basic Operations of Fuzzy Sets The Resolution Theorem A Representation Theorem Extension Principles References DETERMINATION OF MEMBERSHIP FUNCTIONS A General Method for Determining Membership Functions The Three-Phase Method The Incremental Method The Multiphase Fuzzy Statistical Method The Method of Comparisons The Absolute Comparison Method The Set-Valued Statistical Iteration Method Ordering by Precedence Relations The Relative Comparison Method and the Mean Pairwise Comparison Method References MATHEMATICAL ESSENCE AND STRUCTURES OF FEEDFORWARD ARTIFICIAL NEURAL NETWORKS Introduction Mathematical Neurons and Mathematical Neural Networks The Interpolation Mechanism of Feedforward Neural Networks A Three-Layer Feedforward Neural Network with Two Inputs, One Output Analysis of Steepest Descent Learning Algorithms of Feedforward Neural Networks Feedforward Neural Networks with Multi-Input One Output and Their Learning Algorithm Feedforward Neural Networks with One Input Multi-Output and Their Learning Algorithm Feedforward Neural Networks with Multi-Input Multi-Output and Their Learning Algorithm A Note on the Learning Algorithm of Feedforward Neural Networks Conclusions References FUNCTIONAL-LINK NEURAL NETWORKS AND VISUALIZATION MEANS OF SOME MATHEMATICAL METHODS Discussion of the XOR Problem Mathematical Essence of Functional-Link Neural Networks A Visualization Means of Some Mathematical Methods Neural Network Representation of Linear Programming Neural Network Representation of Fuzzy Linear Programming Conclusions References FLAT NEURAL NETWORKS AND RAPID LEARNING ALGORITHMS Introduction The Linear System Equation of the Functional-Link Network Pseudoinverse and Stepwise Updating Training with Weighted Least Square Refine the Model Time-Series Applications Examples and Discussion Conclusions References BASIC STRUCTURE OF FUZZY NEURAL NETWORKS Definition of Fuzzy Neurons Fuzzy Neural Networks A Fuzzy d Learning Algorithm The Convergence of Fuzzy d Learning Rule Conclusions References MATHEMATICAL ESSENCE AND STRUCTURES OF FEEDBACK NEURAL NETWORKS AND WEIGHT MATRIX DESIGN Introduction A General Criterion on the Stability of Networks Generalized Energy Function Learning Algorithm of Discrete Feedback Neural Networks Design Method of Weight Matrices Based on Multifactorial Functions Conclusions References GENERALIZED ADDITIVE MULTIFACTORIAL FUNCTION AND ITS APPLICATIONS TO FUZZY INFERENCE AND NEURAL NETWORKS Introduction On Multifactorial Functions Generalized Additive Weighted Multifactorial Functions Infinite Dimensional Multifactorial Functions M (-,T) and Fuzzy Integral Application in Fuzzy Inference Conclusions References THE INTERPOLATION MECHANISM OF FUZZY CONTROL Preliminary The Interpolation Mechanism of Mamdanian Algorithm with One Input and One Output The Interpolation Mechanism of Mamdanian Algorithm with Two Inputs and One Output A Note on Completeness of Inference Rules The Interpolation Mechanism of (+, o)-Centroid Algorithm The Interpolation Mechanism of Simple Inference Algorithm The Interpolation Mechanism of Function Inference Algorithm A General Fuzzy Control Algorithm Conclusions References THE RELATIONSHIP BETWEEN FUZZY CONTROLLERS AND PID CONTROLLERS Introduction The Relationship of Fuzzy Controllers with One Input One Output and P Controllers The Relationship of Fuzzy Controllers with Two Inputs One Output and PD (or PI) Controllers The Relationship of Fuzzy Controllers with Three Inputs One Output and PID Controllers The Difference Schemes of Fuzzy Controllers with Three Inputs and One Output Conclusions References ADAPTIVE FUZZY CONTROLLERS BASED ON VARIABLE UNIVERSES The Monotonicity of Control Rules and the Monotonicity of Control Functions The Contraction-Expansion Factors of Variable Universes The Structure of Adaptive Fuzzy Controllers Based on Variable Universes Adaptive Fuzzy Controllers with One Input and One Output Adaptive Fuzzy Controll