Introduction to soft computing: neuro-fuzzy and genetic algorithms

Cover......Page 1
Contents......Page 8
Preface......Page 16
Acknowledgements......Page 18
About the Authors......Page 20
 1.1 What is Soft Computing?......Page 22
 1.2 Fuzzy Systems......Page 26
 1.4 Artificial Neural Networks......Page 27
 1.5 Evolutionary Search Strategies......Page 28
  Test Your Knowledge......Page 29
  Bibliography and Historical Notes......Page 30
 2.1 Crisp Sets: A Review......Page 32
  2.1.1 Basic Concepts......Page 33
  2.1.2 Operations on Sets......Page 34
  2.1.3 Properties of Sets......Page 36
 2.2 Fuzzy Sets......Page 37
  2.2.2 Set Membership......Page 38
  2.2.3 Fuzzy Sets......Page 40
  2.2.5 Features of Fuzzy Sets......Page 42
  2.3.1 Some Popular Fuzzy Membership Functions......Page 43
  2.3.2 Transformations......Page 45
  2.3.3 Linguistic Variables......Page 47
 2.4 Operations on Fuzzy Sets......Page 48
  2.5.1 Crisp Relations......Page 52
  2.5.2 Fuzzy Relations......Page 55
  2.5.3 Operations on Fuzzy Relations......Page 57
  2.6.1 Preliminaries......Page 59
  2.6.2 The Extension Principle......Page 62
   Chapter Summary......Page 66
   Solved Problems......Page 67
   Test Your Knowledge......Page 77
   Exercises......Page 79
   Bibliography and Historical Notes......Page 81
Chapter 3:Fuzzy Logic......Page 84
  3.1.1 Propositional Logic......Page 85
  3.1.2 Predicate Logic......Page 90
  3.1.3 Rules of Inference......Page 98
  3.2.1 Fuzzy Truth Values......Page 102
 3.3 Fuzzy Truth in Terms of Fuzzy Sets......Page 104
 3.4 Fuzzy Rules......Page 105
  3.4.1 Fuzzy If-Then......Page 106
  3.4.2 Fuzzy If-Then-Else......Page 107
  3.5.2 Generalized Modus Ponens......Page 109
   Chapter Summary......Page 112
   Solved Problems......Page 114
   Test Your Knowledge......Page 125
   Exercises......Page 128
   Bibliography and Historical Notes......Page 130
 Introduction......Page 132
 4.2 Fuzzification of the Input Variables......Page 133
 4.3 Application of Fuzzy Operators on the Antecedent Parts of the Rules......Page 134
 4.4 Evaluation of the Fuzzy Rules......Page 135
 4.6 Defuzzification of the Resultant Aggregate Fuzzy Set......Page 136
  4.6.1 Centroid Method......Page 137
  4.6.3 Mean-of-Maxima (MoM) Method......Page 139
 4.7 Fuzzy Controllers......Page 141
  4.7.1 Fuzzy Air Conditioner Controller......Page 143
  4.7.2 Fuzzy Cruise Controller......Page 148
  Chapter Summary......Page 151
  Solved Problems......Page 152
  Test Your Knowledge......Page 163
  Exercises......Page 164
  Bibliography and Historical Notes......Page 165
Chapter 5:Rough Sets......Page 166
 5.1 Information Systems and Decision Systems......Page 167
 5.2 Indiscernibility......Page 169
 5.3 Set Approximations......Page 171
 5.4 Properties of Rough Sets......Page 173
 5.5 Rough Membership......Page 174
 5.6 Reducts......Page 175
 Application......Page 178
  Chapter Summary......Page 182
  Solved Problems......Page 183
  Test Your Knowledge......Page 189
  Exercises......Page 191
  Bibliography and Historical Notes......Page 192
Chapter 6:Artificial Neural Networks:Basic Concepts......Page 194
 6.1 Introduction......Page 195
  6.1.1 The Biological Neuron......Page 196
  6.1.2 The Artificial Neuron......Page 197
  6.1.3 Characteristics of the Brain......Page 199
  6.2.1 Pattern Classification......Page 200
  6.2.2 Pattern Association......Page 202
 6.3 The McCulloch–Pitts Neural Model......Page 205
  6.4.1 The Structure......Page 210
  6.4.2 Linear Separability......Page 212
  6.4.3 The XOR Problem......Page 214
 6.5 Neural Network Architectures......Page 215
  6.5.1 Single Layer Feed Forward ANNs......Page 216
  6.5.2 Multilayer Feed Forward ANNs......Page 217
  6.5.3 Competitive Network......Page 218
  6.6.1 Identity Function......Page 219
  6.6.2 Step Function......Page 220
  6.6.3 The Sigmoid Function......Page 221
  6.6.4 Hyperbolic Tangent Function......Page 222
 6.7 Learning by Neural Nets......Page 223
  6.7.1 Supervised Learning......Page 224
  6.7.2 Unsupervised Learning......Page 232
  Chapter Summary......Page 241
  Solved Problems......Page 242
  Test Your Knowledge......Page 247
  Exercises......Page 249
  Bibliography and Historical Notes......Page 251
 7.1 Hebb Nets......Page 254
 7.2 Perceptrons......Page 259
 7.3 Adaline......Page 262
 7.4 Madaline......Page 264
  Solved Problems......Page 272
  Test Your Knowledge......Page 278
  Bibliography and Historical Notes......Page 279
Chapter 8:Pattern Associators......Page 280
  8.1.1 Training......Page 281
  8.1.2 Application......Page 282
  8.1.3 Elimination of Self-connection......Page 283
  8.1.4 Recognition of Noisy Patterns......Page 284
  8.1.5 Storage of Multiple Patterns in an Auto-associative Net......Page 285
 8.2 Hetero-associative Nets......Page 286
  8.2.1 Training......Page 287
 8.3 Hopfield Networks......Page 288
  8.3.2 Training......Page 289
  8.4.1 Architecture......Page 292
  8.4.3 Application......Page 293
 Chapter Summary......Page 299
 Solved Problems......Page 300
 Test Your Knowledge......Page 316
 Answers......Page 317
 Exercises......Page 318
 Bibliography and Historical Notes......Page 319
Chapter 9:Competitive Neural Nets......Page 320
  9.1.2 Application of Maxnet......Page 321
  9.2.1 SOM Architecture......Page 325
  9.2.2 Learning by Kohonen’s SOM......Page 327
  9.2.3 Application......Page 328
  9.3.1 LVQ Learning......Page 332
  9.3.2 Application......Page 334
 9.4 Adaptive Resonance Theory (ART)......Page 339
  9.4.2 Features of ART Nets......Page 340
  9.4.3 Art 1......Page 341
  Chapter Summary......Page 359
  Solved Problems......Page 360
  Test Your Knowledge......Page 386
  Exercises......Page 388
  Bibliography and Historical Notes......Page 389
 10.1 Multi-layer Feedforward Net......Page 392
  10.1.2 Notational Convention......Page 393
  10.1.3 Activation Functions......Page 394
 10.2 The Generalized Delta Rule......Page 396
 10.3 The Backpropagation Algorithm......Page 397
  10.3.1 Choice of Parameters......Page 400
  10.3.2 Application......Page 402
  Chapter Summary......Page 403
  Solved Problems......Page 404
  Test Your Knowledge......Page 412
  Exercises......Page 413
  Bibliography and Historical Notes......Page 414
Chapter 11:Elementary Search Techniques......Page 416
 11.1 State Spaces......Page 417
  11.2.1 Basic Graph Search Algorithm......Page 424
 11.3 Exhaustive Search......Page 425
  11.3.1 Breadth-first Search (BFS)......Page 426
  11.3.2 Depth-first Search (DFS)......Page 428
  11.3.3 Comparison Between BFS and DFS......Page 431
  11.3.4 Depth-first Iterative Deepening......Page 433
  11.3.5 Bidirectional Search......Page 434
  11.4.1 Best-first Search......Page 437
  11.4.3 Hill Climbing......Page 439
  11.4.4 The A/A* Algorithms......Page 447
  11.4.5 Problem Reduction......Page 458
  11.4.6 Means-ends Analysis......Page 467
  11.4.7 Mini-Max Search......Page 471
  11.4.8 Constraint Satisfaction......Page 486
  11.4.9 Measures of Search......Page 497
 11.5 Production Systems......Page 498
  Chapter Summary......Page 507
  Solved Problems......Page 508
  Test Your Knowledge......Page 536
  Exercises......Page 545
  Bibliography and Historical Notes......Page 548
Chapter 12:Advanced Search Strategies......Page 550
  12.1.1 Chromosomes......Page 551
 12.2 Genetic Algorithms (GAs)......Page 552
  12.2.1 Chromosomes......Page 555
  12.2.3 Population......Page 558
  12.2.4 GA Operators......Page 559
  12.2.6 GA Parameters......Page 565
  12.2.7 Convergence......Page 566
  12.3.1 MOO Problem Formulation......Page 567
  12.3.2 The Pareto-optimal Front......Page 568
  12.3.3 Pareto-optimal Ranking......Page 570
  12.3.4 Multi-objective Fitness......Page 572
  12.3.5 Multi-objective GA Process......Page 574
 12.4 Simulated Annealing......Page 575
  Chapter Summary......Page 576
  Solved Problems......Page 577
  Test Your Knowledge......Page 582
  Bibliography and Historical Notes......Page 584
Chapter 13:Hybrid Systems......Page 586
  13.1.1 GA-based Weight Determination of Multi-layerFeed-forward Net......Page 587
  13.1.2 Neuro-evolution of Augmenting Topologies (NEAT)......Page 589
 13.2 Fuzzy-Neural Systems......Page 595
  13.2.1 Fuzzy Neurons......Page 596
  13.2.2 Adaptive Neuro-fuzzy Inference System (ANFIS)......Page 598
 13.3 Fuzzy-genetic Systems......Page 600
  Chapter Summary......Page 602
  Test Your Knowledge......Page 603
  Bibliography and Historical Notes......Page 604
Index......Page 606