Fuzzy neural intelligent systems: mathematical foundation and the applications in engineering

2360_pdf_toc.pdf......Page 2
Fuzzy Neural Intelligent Systems: Mathematical Foundation and the Applications in Engineering......Page 3
Preface......Page 5
Acknowledgments......Page 7
Table of Contents......Page 0
1.1 Definition of Fuzzy Sets......Page 17
1.2 Basic Operations of Fuzzy Sets......Page 22
1.3 The Resolution Theorem......Page 24
1.4 A Representation Theorem......Page 28
1.5 Extension Principle......Page 33
References......Page 38
2.1 A General Method for Determining Membership Functions......Page 39
2.2 The Three-phase Method......Page 43
2.4 The Multiphase Fuzzy Statistical Method......Page 45
2.5.1 Binary Comparisons......Page 47
2.5.2 Preferred Comparisons......Page 48
2.5.3 A Special Case of Preferred Comparisons......Page 49
2.5.4 An Example......Page 50
2.6 The Absolute Comparison Method......Page 51
2.7.2 Basic Steps of Set-valued Statistical Method......Page 54
2.8.2 Creating Order......Page 56
2.8.4 Generalizations......Page 57
2.9.1 The Relative Comparison Method......Page 58
2.9.2 The Mean Pairwise Comparison Method......Page 59
References......Page 62
3.1 Introduction......Page 63
3.2.2 MP Model with Continuous-valued Outputs......Page 64
3.3 The Interpolation Mechanism of Feedforward Neural Networks......Page 68
3.4 A Three-layer Feedforward Neural Network with Two Inputs One Output......Page 72
3.5 Analysis of Steepest Descent Learning Algorithms of Feedforward Neural Networks......Page 74
3.6 Feedforward Neural Networks with Multi-input One Output and Their Learning Algorithm......Page 78
3.7 Feedforward Neural Networks with One Input Multi-output and Their Learning Algorithm......Page 81
3.8 Feedforward Neural Networks with Multi-input Multi-output and Their Learning Algorithm......Page 83
3.9 A Note on the Learning Algorithm of Feedforward Neural Networks......Page 84
3.10 Conclusions......Page 86
References......Page 87
4.1 Discussion of the XOR Problem......Page 88
4.2 Mathematical Essence of Functional-link Neural Networks......Page 91
4.3 As Visualization Means of Some Mathematical Methods......Page 95
4.4 Neural Network Representation of Linear Programming......Page 97
4.5 Neural Network Representation of Fuzzy Linear Programming......Page 102
4.6 Conclusions......Page 103
References......Page 105
5.1 Introduction......Page 106
5.2 The Linear System Equation of the Functional-link Network......Page 107
5.3 Pseudoinverse and Stepwise Updating......Page 109
5.4 Training with Weighted Least Squares......Page 114
5.5 Refine the Model......Page 115
5.6 Time-series Applications......Page 116
5.7 Examples and Discussion......Page 118
5.8 Conclusions......Page 124
References......Page 126
6.1 Definition of Fuzzy Neurons......Page 129
6.2.1 Neural Network Representation of Fuzzy Relation Equations......Page 134
6.2.2 A Fuzzy Neural Network Based on FN......Page 135
6.3 A Fuzzy Learning Algorithm......Page 137
6.4 The Convergence of Fuzzy Learning Rule......Page 139
6.5 Conclusions......Page 140
References......Page 141
7.1 Introduction......Page 142
7.2 A General Criterion on the Stability of Networks......Page 145
7.3 Generalized Energy Function......Page 147
7.4 Learning Algorithm of Discrete Feedback Neural Networks......Page 149
7.5 Design Method of Weight Matrices Based on Multifactorial Functions......Page 151
7.6 Conclusions......Page 153
References......Page 155
8.1 Introduction......Page 156
8.3 Generalized Additive Weighted Multifactorial Functions......Page 157
8.4 Infinite Dimensional Multifactorial Functions......Page 161
8.5 M and Fuzzy Integral......Page 162
8.6 Application in Fuzzy Inference......Page 163
8.7 Conclusions......Page 166
References......Page 167
9.1 Preliminary......Page 168
9.2 The Interpolation Mechanism of Mamdanian Algorithm with One Input and One Output......Page 170
9.3 The Interpolation Mechanism of Mamdanian Algorithm with Two Inputs and One Output......Page 172
9.4 A Note on Completeness of Inference Rules......Page 173
9.5 The Interpolation Mechanism of (+, -)-Centroid Algorithm......Page 174
9.6 The Interpolation Mechanism of Simple Inference Algorithm......Page 175
9.7 The Interpolation Mechanism of Function Inference Algorithm......Page 177
9.8 A General Fuzzy Control Algorithm......Page 178
9.9 Conclusions......Page 179
References......Page 180
10.1 Introduction......Page 181
10.2 The Relationship of Fuzzy Controllers with One Input One Output and P Controllers......Page 182
10.3 The Relationship of Fuzzy Controllers with Two Inputs One Output and PD (or PI) Controllers......Page 185
10.4 The Relationship of Fuzzy Controllers with Three Inputs One Output and PID Controllers......Page 189
10.5.1 Positional Difference Scheme......Page 193
10.5.2 Incremental Difference Scheme......Page 194
10.6 Conclusions......Page 195
References......Page 196
11.1 The Monotonicity of Control Rules and The Monotonicity of Control Functions......Page 197
11.2.1 The Contraction-expansion Factors of Adaptive fuzzy Controllers with One Input and One Output......Page 200
11.2.2 The Contraction-expansion Factors of Adaptive Fuzzy Controllers with Two Inputs and One Output......Page 201
11.3 The Structure of Adaptive Fuzzy Controllers Based on Variable Universes......Page 202
11.4.1 Adaptive Fuzzy Controllers with Potential Heredity......Page 203
11.4.2 Adaptive Fuzzy Controllers with Obvious Heredity......Page 207
11.4.3 Adaptive Fuzzy Controllers with Successively Obvious Heredity......Page 208
11.5 Adaptive fuzzy Controllers with Two Inputs and One Output......Page 209
11.6 Conclusions......Page 211
References......Page 212
12.1 What are “Factors”?......Page 213
12.2 The State Space of Factors......Page 214
12.3.3 Subfactors......Page 216
12.3.5 Disjunction of Factors......Page 217
12.3.9 Atomic Factors......Page 218
12.4 Axiomatic Definition of Factor Spaces......Page 219
12.5 A Note on The Definition of Factor Spaces......Page 220
12.6 Concept Description in a Factor Space......Page 221
12.7 The Projection and Cylindrical Extension of the Representation Extension......Page 223
12.8 Some Properties of the Projection and Cylindrical Extension......Page 225
12.9 Factor Sufficiency......Page 228
12.10 The Rank of a Concept......Page 231
12.11 Atomic Factor Spaces......Page 232
12.12 Conclusions......Page 233
References......Page 234
13.1 Neuron Mechanism of Factor Spaces......Page 235
13.2.1 Threshold Models of Neurons......Page 236
13.2.3 General Threshold Model of Neurons......Page 237
13.2.4 The Models of Neurons Based on Weber-Fechner’s Law......Page 239
13.3 The Models of Neurons Concerned with Time......Page 240
13.4.1 The Excitatory and Inhibitory Mechanism of Neurons......Page 241
13.4.2 The Negative Weights Description of the Inhibitory Mechanism......Page 242
13.4.3 On Fukushima’s Model......Page 243
13.4.4 The Model of Neurons Based on Univariable Weights......Page 244
13.5 Naive Thoughts of Factor Space Canes......Page 245
13.6 Melon-type Factor Space Canes......Page 247
13.7 Chain-type Factor Space Canes......Page 249
13.8 Switch Factors and Growth Relation......Page 250
13.9 Class Partition and Class Concepts......Page 252
13.10 Conclusions......Page 255
References......Page 256
14.1 Introduction......Page 257
14.2 Takagi, Sugeno, and Kang Fuzzy Model......Page 258
14.3 Adaptive Network-based Fuzzy Inference System (ANFIS)......Page 259
14.4 Hybrid Learning Algorithm for ANFIS......Page 260
14.5 Estimation of Lot Processing Time in an IC Fabrication......Page 261
14.5.1 Algorithm 1 : Gauss-Newton-based Levenberg-Marquardt Method......Page 262
14.5.3 Algorithm 3: ANFIS Algorithm......Page 263
14.5.4 Simulation Result......Page 264
14.5.4.2 BP Neural Network Model Construction......Page 265
14.5.4.3 ANFIS Model Construction......Page 266
14.6 Conclusions......Page 267
References......Page 269
15.1 Introduction......Page 271
15.2 Data Preprocessing Algorithms......Page 272
15.2.2 Input Space Reduction......Page 273
Remarks......Page 274
Zscore Normalization......Page 276
Sigmoidal Normalization......Page 277
15.4.1 Example of Noise Reduction Averaging......Page 279
15.4.4 Example of Sigmoidal Normalization......Page 280
15.4.5 The Definitions of Mean and Standard Deviation......Page 281
References......Page 282
16.1 Introduction......Page 283
16.2 Modeling of the Flexible Arm......Page 284
16.3 Simplified Fuzzy Controller......Page 286
16.3.1 Derivation of Simplified Fuzzy Control Law......Page 289
16.3.2 Analysis of Simplified Fuzzy Control Law......Page 291
16.3.3 Neglected Effect in Simplified Fuzzy Control......Page 295
16.4 Self-organizing Fuzzy Control......Page 296
16.4.1 Reference Model......Page 298
16.4.2 Incremental Model......Page 299
16.5 Simulation Results......Page 302
16.6 Conclusions......Page 304
References......Page 309
17.1 Introduction......Page 311
17.2.1 Types of FSRs......Page 313
17.2.2.1 Hardware Devices......Page 314
17.2.3 Interpolation to Increase Resolution......Page 315
17.2.3.2 Polynomial Interpolation......Page 316
17.2.3.4 Fuzzy Interpolation......Page 317
17.3.1 Architecture of the Fuzzy Learning Decision Tree......Page 318
17.3.2 Features Selection......Page 319
17.3.4 Determining Several Points on a Fuzzy Set......Page 321
17.3.6 Learning Procedure of a Decision Tree......Page 322
17.3.7 Comparing to Rule Based Systems......Page 324
17.3.8 Comparison with Artificial Neural Networks......Page 327
17.4 Experiments......Page 331
17.4.1 Experimental Procedures......Page 332
17.4.2 Experiment Results and Discussions......Page 333
17.5 Conclusions......Page 334
References......Page 336
18.1 Introduction......Page 338
18.2 COP Signals Feature Extraction......Page 340
18.2.1 Space Domain Analysis......Page 341
18.2.3 Frequency Domain Analysis......Page 343
18.3 Relationship between COP Signals and FIM Scores......Page 347
18.4.1 Balance Indices Input......Page 357
18.4.2 Knowledge Base......Page 358
18.4.3 Fuzzy Inference Engine......Page 359
Database Setup......Page 360
18.5 Results of Kinetic State Assessment System......Page 363
18.6 Conclusions......Page 364
References......Page 365
19.1 Introduction......Page 367
19.2.1 EMG Signal Processing......Page 368
19.2.2.1 Feature Extraction......Page 369
19.3 DSP-based Prosthetic Controller......Page 371
19.3.1.2 The On-line Stage of the Prosthetic Controller......Page 372
19.3.2.1 Signal Collection......Page 373
19.3.2.2 Signal Processing......Page 374
19.3.2.3 Feature Extraction......Page 375
19.4 Implementation and Results of the DSP-based Controller......Page 377
19.4.2 On-line Stage Implementation......Page 378
19.4.3 On-line Analysis Results......Page 381
19.5 Conclusions......Page 382
References......Page 383