1st Edition
Fuzzy Neural Intelligent Systems Mathematical Foundation and the Applications in Engineering
392 Pages
by
CRC Press
392 Pages
by
CRC Press
Also available as eBook on:
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:
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.
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
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
Biography
Hongxing Li, C.L. Philip Chen, Han-Pang Huang
