ISBN: 3790814385
TITLE: Neuro-Fuzzy Architectures and Hybrid Learning
AUTHOR: Rutkowska
TOC:

Foreword vii
1 Introduction 1
2 Description of Fuzzy Inference Systems 5
2.1 Fuzzy Sets 5
2.1.1 Basic Definitions 5
2.1.2 Operations on Fuzzy Sets 12
2.1.3 Fuzzy Relations 19
2.1.4 Operations on Fuzzy Relations 22
2.2 Approximate Reasoning 25
2.2.1 Compositional Rule of Inference 25
2.2.2 Implications 27
2.2.3 Linguistic Variables 29
2.2.4 Calculus of Fuzzy Rules 34
2.2.5 Granulation and Fuzzy Graphs 37
2.2.6 Computing with Words 41
2.3 Fuzzy Systems 43
2.3.1 Rule-Based Fuzzy Logic Systems 44
2.3.2 The Mamdani and Logical Approaches to Fuzzy Inference 49
2.3.3 Fuzzy Systems Based on the Mamdani Approach 51
2.3.4 Fuzzy Systems Based on the Logical Approach 60
3 Neural Networks and Neuro-Fuzzy Systems 69
3.1 Neural Networks 69
3.1.1 Model of an Artificial Neuron 70
3.1.2 Multi-Layer Perceptron 73
3.1.3 Back-Propagation Learning Method 76
3.1.4 RBF Networks 80
3.1.5 Supervised and Unsupervised Learning 84
3.1.6 Competitive Learning 85
3.1.7 Hebbian Learning Rule 88
3.1.8 Kohonen's Self-Organizing Neural Network 89
3.1.9 Learning Vector Quantization 94
3.1.10 Other Types of Neural Networks 97
3.2 Fuzzy Neural Networks 98
3.3 Fuzzy Inference Neural Networks 101
4 Neuro-Fuzzy Architectures Based on the Mamdani Approach 105
4.1 Basic Architectures 105
4.2 General Form of the Architectures 109
4.3 Systems with Inference Based on Bounded Product 114
4.4 Simplified Architectures 116
4.5 Architectures Based on Other Defuzzification Methods 119
4.5.1 COS-Based Architectures 119
4.5.2 Neural Networks as Defuzzifiers 122
4.6 Architectures of Systems with Non-Singleton Fuzzifier 124
5 Neuro-Fuzzy Architectures Based on the Logical Approach 127
5.1 Mathematical Descriptions of Implication-Based Systems 127
5.2 NOCFS Architectures 133
5.3 OCFS Architectures 136
5.4 Performance Analysis 145
5.5 Computer Simulations 157
5.5.1 Function Approximation 157
5.5.2 Control Examples 158
5.5.3 Classification Problems 160
6 Hybrid Learning Methods 165
6.1 Gradient Learning Algorithms 165
6.1.1 Learning of Fuzzy Systems 166
6.1.2 Learning of Neuro-Fuzzy Systems 171
6.1.3 FLiNN - Architecture Based Learning 174
6.2 Genetic Algorithms 175
6.2.1 Basic Genetic Algorithm 175
6.2.2 Evolutionary Algorithms 181
6.3 Clustering Algorithms 185
6.3.1 Cluster Analysis 185
6.3.2 Fuzzy Clustering 189
6.4 Hybrid Learning 191
6.4.1 Combinations of Gradient Methods, GAs, and Clustering Algorithms 192
6.4.2 Hybrid Algorithms for Parameter Tuning 194
6.4.3 Rule Generation 195
6.5 Hybrid Learning Algorithms for Neuro-Fuzzy Systems 198
6.5.1 Examples of Hybrid Learning Neuro-Fuzzy Systems 199
6.5.2 Description of Two Hybrid Learning Algorithms for Rule Generation 201
6.5.3 Medical Diagnosis Applications 204
7 Intelligent Systems 209
7.1 Artificial and Computational Intelligence 209
7.2 Expert Systems 212
7.2.1 Classical Expert Systems 212
7.2.2 Fuzzy and Neural Expert Systems 214
7.3 Intelligent Computational Systems 217
7.4 Perception-Based Intelligent Systems 220
8 Summary 229
List of Figures 233
List of Tables 239
References 241
END
