Fuzzy Neural Intelligent Systems : Mathematical Foundation and the Applications in Engineering book cover
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Fuzzy Neural Intelligent Systems
Mathematical Foundation and the Applications in Engineering




ISBN 9780849323607
Published September 21, 2000 by CRC Press
392 Pages

 
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Book 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

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