Introduction to soft computing : neuro-fuzzy and genetic algorithms

Soft Computing Is A Branch Of Computer Science That Deals With A Family Of Methods That Imitate Human Intelligence. This Is Done With The Goal Of Creating Tools That Will Contain Some Human-like Capabilities (such As Learning, Reasoning And Decision-making). This Book Covers The Entire Gamut Of Soft Computing, Including Fuzzy Logic, Rough Sets, Artificial Neural Networks, And Various Evolutionary Algorithms. It Offers A Learner-centric Approach Where Each New Concept Is Introduced With Carefully Designed Examples/instances To Train The Learner. 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