Fuzzy Neural Intelligent Systems: Mathematical Foundation and the Applications in Engineering, 1st Edition (Hardback) book cover

Fuzzy Neural Intelligent Systems

Mathematical Foundation and the Applications in Engineering, 1st Edition

By Hongxing Li, C.L. Philip Chen, Han-Pang Huang

CRC Press

392 pages

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Hardback: 9780849323607
pub: 2000-09-21
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Description

Although fuzzy systems and neural networks are central to the field of soft computing, most research work has focused on the development of the theories, algorithms, and designs of systems for specific applications. There has been little theoretical support for fuzzy neural systems, especially their mathematical foundations.

Fuzzy Neural Intelligent Systems fills this gap. It develops a mathematical basis for fuzzy neural networks, offers a better way of combining fuzzy logic systems with neural networks, and explores some of their engineering applications. Dividing their focus into three main areas of interest, the authors give a systematic, comprehensive treatment of the relevant concepts and modern practical applications:

  • Fundamental concepts and theories for fuzzy systems and neural networks.

  • Foundation for fuzzy neural networks and important related topics

  • Case examples for neuro-fuzzy systems, fuzzy systems, neural network systems, and fuzzy-neural systems

    Suitable for self-study, as a reference, and ideal as a textbook, Fuzzy Neural Intelligent Systems is accessible to students with a basic background in linear algebra and engineering mathematics. Mastering the material in this textbook will prepare students to better understand, design, and implement fuzzy neural systems, develop new applications, and further advance the field.

  • Table of Contents

    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 Controllers with Two Inputs and One Output

    Conclusions

    References

    THE BASICS OF FACTOR SPACES

    What are "Factors"?

    The State Space of Factors

    Relations and Operations of Factors

    Axiomatic Definition of Factor Spaces

    A Note on the Definition of Factor Spaces

    Concept Description in a Factor Space

    The Projection and Cylindrical Extension of the Representation Extension

    Some Properties of the Projection and Cylindrical Extension

    Factor Sufficiency

    The Rank of a Concept

    Atomic Factor Spaces

    Conclusions

    References

    NEURON MODELS BASED ON FACTOR SPACES THEORY AND FACTOR SPACE CANES

    Neuron Mechanism of Factor Spaces

    The Models of Neurons without Respect to Time

    The Models of Neurons Concerned with Time

    The Models of Neurons Based in Variable Weights

    Naïve Thoughts of Factor Space Canes

    Melon-Type Factor Space Canes

    Chain-Type Factor Space Canes

    Switch Factors and Growth Relations

    Class Partition and Class Concepts

    Conclusions

    References

    FOUNDATION OF NEURO-FUZZY SYSTEMS AND AN ENGINEERING APPLICATION

    Introduction

    Takagi, Sugeno, and Kang Fuzzy Model

    Adaptive Network-Based Fuzzy Inference System (ANFIS)

    Hybrid Learning Algorithm for ANFIS

    Estimation of Lot Processing Time in an IC Fabrication

    Conclusions

    References

    DATA PREPROCESSING

    Introduction

    Data Preprocessing Algorithms

    Conclusions

    Appendix: MATLAB® Programs

    References

    CONTROL OF A FLEXIBLE ROBOT ARM USING A SIMPLIFIED FUZZY CONTROLLER

    Introduction

    Modeling of the Flexible Arm

    Simplified Fuzzy Controller

    Self-Organizing Fuzzy Control

    Simulation Results

    Conclusions

    References

    APPLICATION OF NEURO-FUZZY SYSTEMS: DEVELOPMENT OF A FUZZY LEARNING DECISION TREE AND APPLICATION TO TACTILE RECOGNITION

    Introduction

    Tactile Sensors and a Tactile Sensing and Recognition System

    Development of a Fuzzy Learning Decision Tree

    Experiments

    Conclusions

    References

    FUZZY ASSESSMENT SYSTEMS OF REHABILITATIVE PROCESS FOR CVA PATIENTS

    Introduction

    COP Signals Feature Extraction

    Relationship between COP Signals and FIM Scores

    Construction of Kinetic State Assessment System

    Results of Kinetic State Assessment System

    Conclusions

    References

    A DSP-BASED NEURAL CONTROLLER FOR A MULTI-DEGREE PROSTHETIC HAND

    Introduction

    EMG Discriminative System

    DSP-Based Prosthetic Controller

    Implementation and Results of the DSP-Based Controller

    Conclusions

    References

    INDEX

    Subject Categories

    BISAC Subject Codes/Headings:
    COM051240
    COMPUTERS / Software Development & Engineering / Systems Analysis & Design
    TEC008000
    TECHNOLOGY & ENGINEERING / Electronics / General