Advanced Fuzzy Systems Design and Applications

1. Fuzzy Sets and Fuzzy Systems.- 1.1 Basics of Fuzzy Sets.- 1.1.1 Fuzzy Sets.- 1.1.2 Fuzzy Operations.- 1.1.3 Fuzzy Relations.- 1.1.4 Measures of Fuzziness.- 1.1.5 Measures of Fuzzy Similarity.- 1.2 Fuzzy Rule Systems.- 1.2.1 Linguistic Variables and Linguistic Hedges.- 1.2.2 Fuzzy Rules for Modeling and Control.- 1.2.3 Mamdani Fuzzy Rule Systems.- 1.2.4 Takagi-Sugeno-Kang Fuzzy Rule Systems.- 1.2.5 Fuzzy Systems are Universal Approximators.- 1.3 Interpretability of Fuzzy Rule System.- 1.3.1 Introduction.- 1.3.2 The Properties of Membership Functions.- 1.3.3 Completeness of Fuzzy Partitions.- 1.3.4 Distinguishability of Fuzzy Partitions.- 1.3.5 Consistency of Fuzzy Rules.- 1.3.6 Completeness and Compactness of Rule Structure.- 1.4 Knowledge Processing with Fuzzy Logic.- 1.4.1 Knowledge Representation and Acquisition with IFTHEN Rules.- 1.4.2 Knowledge Representation with Fuzzy Preference Models.- 1.4.3 Fuzzy Group Decision Making.- 2. Evolutionary Algorithms.- 2.1 Introduction.- 2.2 Generic Evolutionary Algorithms.- 2.2.1 Representation.- 2.2.2 Recombination.- 2.2.3 Mutation.- 2.2.4 Selection.- 2.3 Adaptation and Self-Adaptation in Evolutionary Algorithms.- 2.3.1 Adaptation.- 2.3.2 Self-adaptation.- 2.4 Constraints Handling.- 2.5 Multi-objective Evolution.- 2.5.1 Weighted Aggregation Approaches.- 2.5.2 Population-based Non-Pareto Approaches.- 2.5.3 Pareto-based Approaches.- 2.5.4 Discussions.- 2.6 Evolution with Uncertain Fitness Functions.- 2.6.1 Noisy Fitness Functions.- 2.6.2 Approximate Fitness Functions.- 2.6.3 Robustness Considerations.- 2.7 Parallel Implementations.- 2.8 Summary.- 3. Artificial Neural Networks.- 3.1 Introduction.- 3.2 Feedforward Neural Network Models.- 3.2.1 Multilayer Perceptrons.- 3.2.2 Radial Basis Function Networks.- 3.3 Learning Algorithms.- 3.3.1 Supervised Learning.- 3.3.2 Unsupervised Learning.- 3.3.3 Reinforcement Learning.- 3.4 Improvement of Generalization.- 3.4.1 Heuristic Methods.- 3.4.2 Active Data Selection.- 3.4.3 Regularization.- 3.4.4 Network Ensembles.- 3.4.5 A Priori Knowledge.- 3.5 Rule Extraction from Neural Networks.- 3.5.1 Extraction of Symbolic Rules.- 3.5.2 Extraction of Fuzzy Rules.- 3.6 Interaction between Evolution and Learning.- 3.7 Summary.- 4. Conventional Data-driven Fuzzy Systems Design.- 4.1 Introduction.- 4.2 Fuzzy Inference Based Method.- 4.3 Wang-Mendel’s Method.- 4.4 A Direct Method.- 4.5 An Adaptive Fuzzy Optimal Controller.- 4.6 Summary.- 5.Neural Network Based Fuzzy Systems Design.- 5.1 Neurofuzzy Systems.- 5.2 The Pi-sigma Neurofuzzy Model.- 5.2.1 The Takagi-Sugeno-Kang Fuzzy Model.- 5.2.2 The Hybrid Neural Network Model.- 5.2.3 Training Algorithms.- 5.2.4 Interpretability Issues.- 5.3 Modeling and Control Using the Neurofuzzy System.- 5.3.1 Short-term Precipitation Prediction.- 5.3.2 Dynamic Robot Control.- 5.4 Neurofuzzy Control of Nonlinear Systems.- 5.4.1 Fuzzy Linearization.- 5.4.2 Neurofuzzy Identification of the Subsystems.- 5.4.3 Design of Controller.- 5.4.4 Stability Analysis.- 5.5 Summary.- 6. Evolutionary Design of Fuzzy Systems.- 6.1 Introduction.- 6.2 Evolutionary Design of Flexible Structured Fuzzy Controller..- 6.2.1 A Flexible Structured Fuzzy Controller.- 6.2.2 Parameter Optimization Using Evolution Strategies...- 6.2.3 Simulation Study.- 6.3 Evolutionary Optimization of Fuzzy Rules.- 6.3.1 Genetic Coding of Fuzzy Systems.- 6.3.2 Fitness Function.- 6.3.3 Evolutionary Fuzzy Modeling of Robot Dynamics.- 6.4 Fuzzy Systems Design for High-Dimensional Systems.- 6.4.1 Curse of Dimensionality.- 6.4.2 Flexible Fuzzy Partitions.- 6.4.3 Hierarchical Structures.- 6.4.4 Input Dimension Reduction.- 6.4.5 GA-Based Input Selection.- 6.5 Summary.- 7. Knowledge Discovery by Extracting Interpretable Fuzzy Rules.- 7.1 Introduction.- 7.1.1 Data, Information and Knowledge.- 7.1.2 Interpretability and Knowledge Extraction.- 7.2 Evolutionary Interpretable Fuzzy Rule Generation.- 7.2.1 Evolution Strategy for Mixed Parameter Optimization.- 7.2.2 Genetic Representation of Fuzzy Systems.- 7.2.3 Multiobjective Fuzzy Systems Optimization.- 7.2.4 An Example: Fuzzy Vehicle Distance Controller.- 7.3 Interactive Co-evolution for Fuzzy Rule Extraction.- 7.3.1 Interactive Evolution.- 7.3.2 Co-evolution.- 7.3.3 Interactive Co-evolution of Interpretable Fuzzy Systems.- 7.4 Fuzzy Rule Extraction from RBF Networks.- 7.4.1 Radial-Basis-Function Networks and Fuzzy Systems.- 7.4.2 Fuzzy Rule Extraction by Regularization.- 7.4.3 Application Examples.- 7.5 Summary.- 8. Fuzzy Knowledge Incorporation into Neural Networks.- 8.1 Data and A Priori Knowledge.- 8.2 Knowledge Incorporation in Neural Networks for Control.- 8.2.1 Adaptive Inverse Neural Control.- 8.2.2 Knowledge Incorporation in Adaptive Neural Control.- 8.3 Fuzzy Knowledge Incorporation By Regularization.- 8.3.1 Knowledge Representation with Fuzzy Rules.- 8.3.2 Regularized Learning.- 8.4 Fuzzy Knowledge as A Related Task in Learning.- 8.4.1 Learning Related Tasks.- 8.4.2 Fuzzy Knowledge as A Related Task.- 8.5 Simulation Studies.- 8.5.1 Regularized Learning.- 8.5.2 Multi-task Learning.- 8.6 Summary.- 9. Fuzzy Preferences Incorporation into Multi-objective Optimization.- 9.1 Multi-objective Optimization and Preferences Handling.- 9.1.1 Multi-objective Optimization.- 9.1.2 Incorporation of Fuzzy Preferences.- 9.2 Evolutionary Dynamic Weighted Aggregation.- 9.2.1 Conventional Weighted Aggregation for MOO.- 9.2.2 Dynamically Weighted Aggregation.- 9.2.3 Archiving of Pareto Solutions.- 9.2.4 Simulation Studies.- 9.2.5 Theoretical Analysis.- 9.3 Fuzzy Preferences Incorporation in MOO.- 9.3.1 Converting Fuzzy Preferences into Crisp Weights.- 9.3.2 Converting Fuzzy Preferences into Weight Intervals.- 9.4 Summary.- References.