ISBN: 3790815373
TITLE: Advanced Fuzzy Systems Design and Applications
AUTHOR: Jin
TOC:

1. Fuzzy Sets and Fuzzy Systems 1
1.1 Basics of Fuzzy Sets 1
1.1.1 Fuzzy Sets 1
1.1.2 Fuzzy Operations 7
1.1.3 Fuzzy Relations 10
1.1.4 Measures of Fuzziness 13
1.1.5 Measures of Fuzzy Similarity 15
1.2 Fuzzy Rule Systems 16
1.2.1 Linguistic Variables and Linguistic Hedges 16
1.2.2 Fuzzy Rules for Modeling and Control 19
1.2.3 Mamdani Fuzzy Rule Systems 25
1.2.4 Takagi-Sugeno-Kang Fuzzy Rule Systems 26
1.2.5 Fuzzy Systems are Universal Approximators 27
1.3 Interpretability of Fuzzy Rule System 29
1.3.1 Introduction 29
1.3.2 The Properties of Membership Functions 30
1.3.3 Completeness of Fuzzy Partitions 30
1.3.4 Distinguishability of Fuzzy Partitions 33
1.3.5 Consistency of Fuzzy Rules 34
1.3.6 Completeness and Compactness of Rule Structure 37
1.4 Knowledge Processing with Fuzzy Logic 37
1.4.1 Knowledge Representation and Acquisition with IF-THEN Rules 37
1.4.2 Knowledge Representation with Fuzzy Preference Models 42
1.4.3 Fuzzy Group Decision Making 45
2. Evolutionary Algorithms 49
2.1 Introduction 49
2.2 Generic Evolutionary Algorithms 49
2.2.1 Representation 50
2.2.2 Recombination 53
2.2.3 Mutation 54
2.2.4 Selection 55
2.3 Adaptation and Self-Adaptation in Evolutionary Algorithms 55
2.3.1 Adaptation 55
2.3.2 Self-adaptation 56
2.4 Constraints Handling 58
2.5 Multi-objective Evolution 60
2.5.1 Weighted Aggregation Approaches 61
2.5.2 Population-based Non-Pareto Approaches 62
2.5.3 Pareto-based Approaches 62
2.5.4 Discussions 63
2.6 Evolution with Uncertain Fitness Functions 64
2.6.1 Noisy Fitness Functions 64
2.6.2 Approximate Fitness Functions 64
2.6.3 Robustness Considerations 68
2.7 Parallel Implementations 69
2.8 Summary 70
3. Artificial Neural Networks 73
3.1 Introduction 73
3.2 Feedforward Neural Network Models 73
3.2.1 Multilayer Perceptrons 74
3.2.2 Radial Basis Function Networks 75
3.3 Learning Algorithms 75
3.3.1 Supervised Learning 76
3.3.2 Unsupervised Learning 78
3.3.3 Reinforcement Learning 79
3.4 Improvement of Generalization 80
3.4.1 Heuristic Methods 81
3.4.2 Active Data Selection 81
3.4.3 Regularization 82
3.4.4 Network Ensembles 84
3.4.5 A Priori Knowledge 85
3.5 Rule Extraction from Neural Networks 86
3.5.1 Extraction of Symbolic Rules 86
3.5.2 Extraction of Fuzzy Rules 87
3.6 Interaction between Evolution and Learning 89
3.7 Summary 90
4. Conventional Data-driven Fuzzy Systems Design 93
4.1 Introduction 93
4.2 Fuzzy Inference Based Method 94
4.3 Wang-Mendel's Method 100
4.4 A Direct Method 102
4.5 An Adaptive Fuzzy Optimal Controller 105
4.6 Summary 110
5. Neural Network Based Fuzzy Systems Design 111
5.1 Neurofuzzy Systems 111
5.2 The Pi-sigma Neurofuzzy Model 114
5.2.1 The Takagi-Sugeno-Kang Fuzzy Model 114
5.2.2 The Hybrid Neural Network Model 115
5.2.3 Training Algorithms 116
5.2.4 Interpretability Issues 120
5.3 Modeling and Control Using the Neurofuzzy System 123
5.3.1 Short-term Precipitation Prediction 123
5.3.2 Dynamic Robot Control 124
5.4 Neurofuzzy Control of Nonlinear Systems 130
5.4.1 Fuzzy Linearization 132
5.4.2 Neurofuzzy Identification of the Subsystems 135
5.4.3 Design of Controller 137
5.4.4 Stability Analysis 138
5.5 Summary 141
6. Evolutionary Design of Fuzzy Systems 143
6.1 Introduction 143
6.2 Evolutionary Design of Flexible Structured Fuzzy Controller 145
6.2.1 A Flexible Structured Fuzzy Controller 145
6.2.2 Parameter Optimization Using Evolution Strategies 146
6.2.3 Simulation Study 147
6.3 Evolutionary Optimization of Fuzzy Rules 148
6.3.1 Genetic Coding of Fuzzy Systems 148
6.3.2 Fitness Function 152
6.3.3 Evolutionary Fuzzy Modeling of Robot Dynamics 153
6.4 Fuzzy Systems Design for High-Dimensional Systems 160
6.4.1 Curse of Dimensionality 160
6.4.2 Flexible Fuzzy Partitions 161
6.4.3 Hierarchical Structures 163
6.4.4 Input Dimension Reduction 164
6.4.5 GA-Based Input Selection 169
6.5 Summary 171
7. Knowledge Discovery by Extracting Interpretable Fuzzy Rules 173
7.1 Introduction 173
7.1.1 Data, Information and Knowledge 173
7.1.2 Interpretability and Knowledge Extraction 174
7.2 Evolutionary Interpretable Fuzzy Rule Generation 175
7.2.1 Evolution Strategy for Mixed Parameter Optimization 176
7.2.2 Genetic Representation of Fuzzy Systems 177
7.2.3 Multiobjective Fuzzy Systems Optimization 178
7.2.4 An Example: Fuzzy Vehicle Distance Controller 180
7.3 Interactive Co-evolution for Fuzzy Rule Extraction 184
7.3.1 Interactive Evolution 184
7.3.2 Co-evolution 186
7.3.3 Interactive Co-evolution of Interpretable Fuzzy Systems 186
7.4 Fuzzy Rule Extraction from RBF Networks 187
7.4.1 Radial-Basis-Function Networks and Fuzzy Systems 187
7.4.2 Fuzzy Rule Extraction by Regularization 191
7.4.3 Application Examples 196
7.5 Summary 203
8. Fuzzy Knowledge Incorporation into Neural Networks 205
8.1 Data and A Priori Knowledge 205
8.2 Knowledge Incorporation in Neural Networks for Control 207
8.2.1 Adaptive Inverse Neural Control 207
8.2.2 Knowledge Incorporation in Adaptive Neural Control 208
8.3 Fuzzy Knowledge Incorporation By Regularization 210
8.3.1 Knowledge Representation with Fuzzy Rules 210
8.3.2 Regularized Learning 213
8.4 Fuzzy Knowledge as A Related Task in Learning 216
8.4.1 Learning Related Tasks 216
8.4.2 Fuzzy Knowledge as A Related Task 216
8.5 Simulation Studies 217
8.5.1 Regularized Learning 218
8.5.2 Multi-task Learning 219
8.6 Summary 221
9. Fuzzy Preferences Incorporation into Multi-objective Optimization 223
9.1 Multi-objective Optimization and Preferences Handling 223
9.1.1 Multi-objective Optimization 223
9.1.2 Incorporation of Fuzzy Preferences 225
9.2 Evolutionary Dynamic Weighted Aggregation 226
9.2.1 Conventional Weighted Aggregation for MOO 227
9.2.2 Dynamically Weighted Aggregation 228
9.2.3 Archiving of Pareto Solutions 230
9.2.4 Simulation Studies 230
9.2.5 Theoretical Analysis 237
9.3 Fuzzy Preferences Incorporation in MOO 247
9.3.1 Converting Fuzzy Preferences into Crisp Weights 247
9.3.2 Converting Fuzzy Preferences into Weight Intervals 249
9.4 Summary 252
References 268
Index 269
END
