Genetic Fuzzy Systems

The following sections are included:

• Foreword

• Preface

• Contents

The following sections are included:

• Framework: Fuzzy Logic and Fuzzy Systems

• Mamdani Fuzzy Rule-Based Systems
  • The knowledge base of Mamdani fuzzy rule-based systems
  • The inference engine of Mamdani fuzzy rule-based systems
    • The fuzzification interface
    • The inference system
    • The defuzzification interface
  • Example of application
  • Design of the inference engine
  • Advantages and drawbacks of Mamdani-type fuzzy rule-based systems
  • Variants of Mamdani fuzzy rule-based systems
    • DNF Mamdani fuzzy rule-based systems
    • Approximate Mamdani-type fuzzy rule-based systems

• Takagi–Sugeno–Kang Fuzzy Rule-Based Systems

• Generation of the Fuzzy Rule Set
  • Design tasks for obtaining the fuzzy rule set
  • Kinds of information available to define the fuzzy rule set
  • Generation of linguistic rules
  • Generation of approximate Mamdani-type fuzzy rules
  • Generation of TSK fuzzy rules
  • Basic properties of fuzzy rule sets
    • Completeness of a fuzzy rule set
    • Consistency of a fuzzy rule set
    • Low complexity of a fuzzy rule set
    • Redundancy of a fuzzy rule set

• Applying Fuzzy Rule-Based Systems
  • Fuzzy modelling
    • Benefits of using fuzzy rule-based systems for modelling
    • Relationship between fuzzy modelling and system identification
    • Some applications of fuzzy modelling
  • Fuzzy control
    • Advantages of fuzzy logic controllers
    • Differences between the design of fuzzy logic controllers and fuzzy models
    • Some applications of fuzzy control
  • Fuzzy classification
    • Advantages of using fuzzy rule-based systems for classification
    • Components and design of fuzzy rule-based classification systems
    • Some applications of fuzzy classification

The following sections are included:

• Conceptual Foundations of Evolutionary Computation

• Genetic Algorithms
  • Main characteristics
  • Schema theorem
  • Extensions to the simple genetic algorithm
    • Genetic encoding of solutions
    • Fitness scaling
    • Selection and replacement schemes
    • Niching genetic algorithms
    • Recombination
  • Real-coded genetic algorithms
    • Recombination in real-coded genetic algorithms
    • Mutation in real-coded genetic algorithms
  • Messy genetic algorithms
    • Under- and over-specification
    • Genetic operators

• Other Evolutionary Algorithms
  • Evolution strategies
  • Evolutionary programming
  • Genetic programming

The following sections are included:

• Soft Computing

• Hybridisation in Soft Computing
  • Fuzzy logic and neural networks
    • Neuro-fuzzy systems
    • Fuzzy-neural networks
  • Neural networks and evolutionary computation
    • Genetic algorithms for training neural networks
    • Genetic algorithms for learning the topology of the network
  • Genetic algorithms and probabilistic reasoning

• Integration of Evolutionary Algorithms and Fuzzy Logic
  • Fuzzy evolutionary algorithms
    • Adaptation of genetic algorithm control parameters
    • Genetic algorithm components based on fuzzy tools

• Genetic Fuzzy Systems
  • Genetic fuzzy rule-based systems
  • Defining the phenotype space for a genetic fuzzy rule-based system
    • Genetic tuning of the data base
    • Genetic learning of the rule base
    • Genetic learning of the knowledge base
    • A phenotype space of rules or rule bases/knowledge bases
  • From phenotype to genotype spaces
  • Generating new genetic material
  • Evaluating the genetic material
  • The cooperation versus competition problem

The following sections are included:

• Tuning of Fuzzy Rule-Based Systems
  • Tuning of scaling functions
    • Linear contexts
    • Non-linear contexts
  • Tuning of membership functions
  • Tuning of fuzzy rules

• Genetic Tuning of Scaling Functions

• Genetic Tuning of Membership Functions of Mamdani Fuzzy Rule-Based Systems
  • Shape of the membership functions
    • Piece-wise linear functions
    • Differentiable functions
  • Scope of the semantics
    • Tuning of descriptive Mamdani fuzzy rule-based systems
    • Tuning of approximate Mamdani fuzzy rule-based systems
  • Example: genetic tuning processes of Mamdani-type fuzzy rule sets
    • Common aspects of both genetic tuning processes
    • The approximate genetic tuning process
    • The descriptive genetic tuning process

• Genetic Tuning of TSK Fuzzy Rule Sets
  • Genetic tuning of TSK rule consequent parameters
  • Example: the evolutionary tuning process of MOGUL for TSK knowledge bases
    • Representation
    • Initial population
    • Genetic operators

The following sections are included:

• Genetic Learning Processes. Introduction

• The Michigan Approach. Classifier Systems
  • The performance system
  • The credit assignment system
  • The classifier discovery system
  • Basic operations of a classifier system
  • Classifier system extensions
    • ZCS and XCS
    • Anticipatory Classifier System

• The Pittsburgh Approach
  • The population of rule bases
  • The evaluation system
  • The rule base discovery system
  • Representation
  • Genetic learning processes based on the Pittsburgh approach
    • GABIL learning system
    • GIL learning system
    • Corcoran and Sen's learning system

• The Iterative Rule Learning Approach

The following sections are included:

• Basic Features of Fuzzy Classifier Systems

• Fuzzy Classifier Systems for Learning Rule Bases
  • Valenzuela-Rendón's FCS: Introducing reinforcement learning
  • Fuzzy classifier systems for learning fuzzy classification rules
    • Coding the linguistic classification rules and initial population
    • Evaluation of each rule
    • Genetic operations for generating new rules
    • Rule replacement and termination test
    • Algorithm
    • Fuzzy classifier system for learning classification rules: extensions

• Fuzzy Classifier Systems for Learning Fuzzy Rule Bases
  • Parodi and Bonelli's fuzzy classifier system for approximate fuzzy rule bases
    • Basic model
    • Description of the algorithm
  • Fuzzy classifier system for on-line learning of approximate fuzzy control rules
    • The proposed fuzzy classifier system
    • On-line learning of fuzzy rules using the Limbo

The following sections are included:

• Coding Rule Bases as Chromosomes
  • Positional semantics
    • Decision tables
    • Relational matrices
    • TSK-type rules
• Non-positional semantics (list of rules)
  • Rules of fixed length
  • Rules of variable length
  • Rules of approximate type

• Multi-chromosome Genomes (Coding Knowledge Bases)
  • Representation
  • Operators

• Examples
  • A method to learn decision tables
  • A method to learn relational matrices
  • A method to learn TSK-type knowledge bases
  • A method to learn DNF Mamdani-type knowledge bases (with rules of fixed length)
  • A method to learn DNF Mamdani-type rule bases (with rules of variable length)
  • A method to learn approximate Mamdani-type fuzzy rule bases

The following sections are included:

• Coding the Fuzzy Rules
  • Coding linguistic rules
  • Coding approximate Mamdani-type fuzzy rules
  • Coding TSK fuzzy rules

• Learning Fuzzy Rules under Competition
  • The fuzzy rule generating method
    • Different criteria for the fitness function of the generating method
    • Some examples of fuzzy rule generating methods
• The iterative covering method
  • The iterative covering method of MOGUL
  • The iterative covering method of SLAVE

• Post-Processing: Refining Rule Bases under Cooperation
  • The post-processing algorithm of MOGUL
    • The basic genetic simplification process
    • The multi-simplification process
  • The post-processing algorithm of SLAVE

• Inducing Cooperation in the Fuzzy Rule Generation Stage
  • Inducing cooperation in descriptive fuzzy rule generation processes: the proposals of SLAVE
    • Cooperation between rules in SLAVE for crisp consequent domain problems
    • Cooperation between rules in SLAVE for fuzzy consequent domain problems
  • Inducing cooperation in approximate fuzzy rule generation processes: the low niche interaction rate considered in MOGUL
  • Inducing cooperation in TSK fuzzy rule generation processes: the local error measure considered in MOGUL

• Examples
  • MOGUL
  • SLAVE

The following sections are included:

• Designing Fuzzy Rule-Based Systems with Genetic Programming
  • Learning rule bases with genetic programming
    • Encoding rule bases
    • Necessity of a typed-system
    • Generating rule bases
  • Learning knowledge bases with genetic programming

• Genetic Selection of Fuzzy Rule Sets
  • Genetic selection from a set of candidate fuzzy rules
  • Genetic selection of rule bases integrating linguistic modifiers to change the membership function shapes
    • The use of linguistic modifiers to adapt the membership function shapes
    • A genetic multi-selection process considering linguistic hedges
    • The basic genetic selection method
    • Algorithm of the genetic multi-selection process
    • Parametric extension
  • ALM: Accurate linguistic modelling using genetic selection
    • Some important remarks about ALM
    • A linguistic modelling process based on ALM
  • Genetic selection with hierarchical knowledge bases
    • Hierarchical knowledge base philosophy
    • System modelling with hierarchical knowledge bases

• Learning the Knowledge Base via the Genetic Derivation of the Data Base
  • Learning the knowledge base by deriving the data base
  • Genetic learning of membership functions
    • Genetic learning of isosceles triangular-shaped membership functions
    • Genetic learning of membership functions with implicit granularity learning
    • Genetic learning of the granularity and the membership functions
    • Genetic algorithm-based fuzzy partition learning method for pattern classification problems
  • Genetic learning of non-linear contexts
    • Genetic learning process for the scaling factors, granularity and non-linear contexts

• Other Genetic-Based Machine Learning Approaches
  • Genetic integration of multiple knowledge bases
  • Flexibility, completeness, consistency, compactness and complexity reduction
    • Evolutionary generation of flexible, complete, consistent and compact fuzzy rule-based systems
    • Genetic complexity reduction and interpretability improvement
  • Hierarchical distributed genetic algorithms: designing fuzzy rule-based systems using a multi-resolution search paradigm
  • Parallel genetic algorithm to learn knowledge bases with different granularity levels
  • Modular and hierarchical evolutionary design of fuzzy rule-based systems
  • VEGA: virus-evolutionary genetic algorithm to learn TSK fuzzy rule sets
    • Preliminaries: virus theory of evolution
    • Virus-evolutionary genetic algorithm architecture
    • Virus infection operators
    • The VEGA genetic fuzzy rule-based system
  • Nagoya approach: genetic-based machine learning algorithm using mechanisms of genetic recombination in bacteria genetics
    • Bacterial genetics
    • Nagoya approach: algorithm description
    • Nagoya approach: extensions
  • Learning fuzzy rules with the use of DNA coding
  • Hybrid fuzzy genetic-based machine learning algorithm (Pittsburgh and Michigan) to designing compact fuzzy rule-based systems

The following sections are included:

• Genetic Fuzzy Neural Networks
  • Genetic learning of fuzzy weights
  • Genetic learning of radial basis functions and weights
  • Genetic learning of fuzzy rules through the connection weights
  • Combination of genetic algorithms and delta rule for coarse and fine tuning of a fuzzy-neural network

• Genetic Fuzzy Clustering
  • Introduction to the clustering problem
  • Hard clustering
  • Fuzzy clustering
  • Different applications of evolutionary algorithms to fuzzy clustering
    • Prototype-based genetic fuzzy clustering
    • Fuzzy partition-based genetic fuzzy clustering
    • Genetic fuzzy clustering by defining the distance norm
    • Pure genetic fuzzy clustering

• Genetic Fuzzy Decision Trees
  • Decision trees
  • Fuzzy decision trees
  • Optimising Fuzzy Decision Trees

The following sections are included:

• Classification
  • Genetic fuzzy rule-based systems to learn fuzzy classification rules: revision
  • Diagnosis of myocardial infarction
  • Breast cancer diagnosis
    • Fuzzy rule-based classification system parameters
    • Genetic learning approach
    • Results

• System Modelling
  • Power distribution problems in Spain
    • Computing the length of low voltage lines
    • Computing the maintenance costs of medium voltage line
  • The rice taste evaluation problem
  • Dental development age prediction

• Control Systems
  • The cart-pole balancing system
    • Goal and fitness function
    • Some results
  • A diversification problem
  • Supervision of fossil power plant operation
    • Problem statement
    • Genetic fuzzy rule-based system
    • Application results

• Robotics
  • Behaviour-based robotics
  • Evolutionary robotics
  • Robotic platform
  • Perception of the environment
  • Fuzzy logic controller
  • Genetic fuzzy rule-based system

The following sections are included:

• Bibliography

• Acronyms

• Index