Computational Intelligence, Theory and Applications (eBook)

International Conference 9th Fuzzy Days in Dortmund, Germany, Sept. 18-20, 2006 Proceedings

Bernd Reusch (Herausgeber)

eBook Download: PDF

2006
XXX, 802 Seiten
Springer Berlin (Verlag)
978-3-540-34783-5 (ISBN)

Infos

This book constitutes the refereed proceedings of the 9th Dortmund Fuzzy Days, Dortmund, Germany, 2006. This conference has established itself as an international forum for the discussion of new results in the field of Computational Intelligence. The papers presented here, all thoroughly reviewed, are devoted to foundational and practical issues in fuzzy systems, neural networks, evolutionary algorithms, and machine learning and thus cover the whole range of computational intelligence.

Inhalt

Preface 6
Programme Chairs 7
Programme Committee 7
Local Organization 7
Contents 8
List of Contributors 18
Plenary Talk 31
From Search Engines to Question-Answering Systems: The Problems of World Knowledge, Relevance, Deduction, and Precisiation 31
Invited Session: Fuzzy Multiperson and Multicriteria Decisions Modelling 35
A Fuzzy Approach to Optimal R& D Project Portfolio Selection
1 Introduction 35
2 Real Options for R& D Portfolios
3 A Hybrid Approach to Real Option Valuation 39
4 A Possibilistic Approach to R& D Portfolio Selection
5 Summary 42
References 42
Choquet Integration and Correlation Matrices in Fuzzy Inference Systems 45
References 47
Linguistic Summarization of Some Static and Dynamic Features of Consensus Reaching 49
1 Introduction 49
2 Degrees of Consensus under Fuzzy Preferences and a Fuzzy Majority 50
3 A Consensus Reaching Process and Linguistic Data Summarization 52
4 A Dynamic View of Consensus Reaching 55
5 Concluding Remarks 56
References 56
Consistency for Nonadditive Measures: Analytical and Algebraic Methods 59
1 Choosing Among Several Alternatives 59
2 Fuzzy Measures on the Set of Objectives 60
3 Aggregation of Fuzzy Measures with Respect to a t- Conorm 62
4 Algebraic and Geometric Representations by Means of Hypergroups 64
5 Assessment of Consistent Measures to the Objectives 67
6 An Algorithm to Compare the Alternatives 69
7 An Extension to the Fuzzy Measures of Type 2 69
References 70
Neural Nets 71
Neuro-Fuzzy Kolmogorov’s Network with a Modified Perceptron Learning Rule for Classification Problems 71
1 Introduction 71
2 Network Architecture 72
3 Learning Algorithm 73
4 Experiments 76
5 Conclusion 78
References 79
A Self-Tuning Controller for Teleoperation System using Evolutionary Learning Algorithms in Neural Networks 81
1 Introduction 81
2 Neural Controller and Evolutionary Programming 84
3 Fitness Function 86
4 Simulation Results 87
5 Conclusion 89
References 89
A Neural-Based Method for Choosing Embedding Dimension in Chaotic Time Series Analysis 91
1 Introduction 91
2 Characteristics of Chaotic Systems 93
3 Maximal Lyapunov Exponent 93
4 Phase Space Reconstruction, Embedding Theorems 94
5 Choosing the Delay Time 95
6 Embedding Dimension Estimation 96
7 Predictive Method for Minimum Embedding Dimension Estimation 97
8 Indirect Method for Maximal Lyapunov Estimation 99
9 Simulation Results 99
10 Conclusion 102
References 103
On Classification of Some Hop.eld-Type Learning Rules via Stability Measures 105
1 Introduction 105
2 The Hopfield Model and Its Storage Capacity 106
3 Some Learning Methods and Architectures 106
4 Empirical Analysis of Storage Capacity 108
5 Classification of Hopfield Memories via a Stability Measure 109
6 Classification of the Models via Experimental Analysis 110
7 Conclusion 112
References 113
Applications I 115
A New Genetic Based Algorithm for Channel Assignment Problems 115
1 Introduction 115
2 Channel Assignment Problem Formulation 116
3 Conventional Genetic Algorithm 117
4 Our New Method Based on Genetic Algorithm 117
5 Simulation Results 119
6 Conclusion 120
Acknowledgment 121
References 121
Max-Product Fuzzy Relational Equations as Inference Engine for Prediction of Textile Yarn Properties 123
1 Introduction 123
2 Max-Prod Fuzzy Linear Equations as Inference Engine 124
3 Implementation Methodology 127
4 Numerical Example 130
5 Discussion 131
6 Conclusions 132
Acknowledgments 132
References 132
Automatic Defects Classification and Feature Extraction Optimization 135
1 Motivation 135
2 Automatic Classification System 136
3 Feature Extraction Technologies 136
4 Classification Results 140
5 Optimization of Feature Extraction 140
6 Summary 145
References 145
Short-Term Load Forecasting in Power System Using Least Squares Support Vector Machine 147
1 Introduction 147
2 Review of LS-SVM 148
3 Short-Term Forecasting Using LS-SVM 150
4 Examples 152
5 Conclusions 154
6 Copyright Form 154
References 155
Appendix: Springer-Author Discount 156
Plenary Talk 157
Fifteen Years of Fuzzy Logic in Dortmund 157
1 Introduction 157
2 Basic Operations 158
3 Fuzzy Logic 159
4 Inference Methods 160
5 Fuzzy Relations 161
6 Fuzzy Sets, Related Concepts, and Applications 161
7 Concluding Remarks 163
References 165
Invited Session: Intuitionistic Fuzzy Sets and Generalized Nets I 169
Intuitionistic Fuzzy Graphs 169
1 Introduction 169
2 Preliminaries 170
3 Properties 173
4 Conclusion 179
Acknowledgement 179
References 179
On Some Intuitionistic Properties of Intuitionistic Fuzzy Implications and Negations 181
1 Introduction: on Some Previous Results 181
2 Main Results 182
3 Conclusion 186
References 188
On Intuitionistic Fuzzy Negations 189
1 Introduction: on Some Previous Results 189
2 Main Results 191
3 Conclusion: a New Argument that the Intuitionistic Fuzzy Sets Have Intuitionistic Nature 195
References 197
Invited Session: Soft Computing Techniques for Reputation and Trust I 199
A Simulation Model for Trust and Reputation System Evaluation in a P2P Network 199
1 Model Requirements 200
2 The Peer Behavior Model 205
3 The Simulation Model 206
4 Conclusions 209
References 209
A Fuzzy Trust Model Proposal to Ensure the Identity of a User in Time 211
1 Introduction 211
2 User Authentication Systems and Their Trustfulness 212
3 Architecture of the Model 216
4 Trust Model Rules 218
5 Conclusions 219
Acknowledgments 220
References 220
Quantification of the Effectiveness of the Markov Model for Trustworthiness Prediction 221
1 Introduction 221
2 Exogenous Parameters Used in the Simulation 223
3 Behaviors of the Agents in the Prototype Simulation 223
4 Effectiveness of Markov Model on Trust Based Decision Making 225
5 Conclusions and Future Work 229
References 230
Applications II 231
Fuzzy-Genetic Methodology for Web-based Computed- Aided Diagnosis in Medical Applications 231
1 Introduction 231
2 Materials and Methods 233
3 Case Study 239
4 Concluding Remarks 242
5 Acknowledgments 242
References 242
Weight Optimization for Loan Risk Estimation with Genetic Algorithm 245
1 Introduction 245
2 GA in Weight Optimization Task 246
3 An Individual Fitness 247
4 Crossover 248
5 Mutation 248
6 Experimental Results 249
7 Conclusions 250
Acknowledgments 250
References 250
A Fuzzy Feature Extractor Neural Network and its Application in License Plate Recognition 253
1 Introduction 253
2 Feature Extractor Fuzzy Neural Network 254
3 License Plate Type Recognition 255
4 Results 256
References 257
Invited Session: Intuitionistic Fuzzy Sets and Generalized Nets II 259
Nearest Interval Approximation of an Intuitionistic Fuzzy Number 259
1 Intuitionistic Fuzzy Numbers 259
2 Distances between Intuitionistic Fuzzy Numbers 261
3 Nearest Interval Approximation of Intuitionistic Fuzzy Numbers 262
4 Properties of the Nearest Intervals Approximation of Intuitionistic Fuzzy Numbers 268
References 270
On Intuitionistic Fuzzy Expert Systems With Temporal Parameters 271
1 Introduction 271
2 Short Remarks on IFL 271
3 Main Results 275
4 Conclusion 279
References 279
Generalized Fuzzy Cardinalities of IF Sets 281
1 Introduction 281
2 Preliminaries 281
3 Fuzzy Cardinality of Fuzzy Sets 285
4 Fuzzy Cardinality of IF Sets 287
Conclusion 290
References 291
Invited Session: Soft Computing Techniques for Reputation and Trust II 293
Towards Usage Policies for Fuzzy Inference Methodologies for Trust and QoS Assessment 293
1 Related Work 294
2 Fuzzy Trust and QoS Assessment 295
3 Fuzzy Rules and Inference Methodologies 297
4 Usage Policies for Fuzzy Inference Methodologies 299
5 Conclusion 302
References 303
Simulating a Trust-Based Peer-to-Peer Metadata Publication Center 305
1 Introduction 305
2 The Trust Layer Architecture 306
3 Setting a Trust Layer Simulator 308
4 Some Examples of Simulations 309
Acknowledgments 309
References 310
The Complex Facets of Reputation and Trust 311
1 Introduction 311
2 Fundamentals 312
3 State-of-the-Art 312
4 Propagation of Reputation Information 315
5 Bounded Rationality 317
6 Behavioral Evolution 318
7 Second-Order Defection Problem 319
8 Inhomogeneous Interactions 320
9 Identity Stability 321
10 Conclusions 322
References 323
Theory I 325
Fuzzy Covering Relation and Ordering: An Abstract Approach 325
1 Covering and Order in Crisp Case 325
2 Lattice-Valued Fuzzy Order and Covering 327
3 Examples 329
4 Conclusion 330
Acknowledgment 330
References 330
Measures of Differentiability 331
1 Introduction and Preliminaries 331
2 Measures of Differentiability 333
Acknowledgment 336
References 336
Lipschitz Continuity of Triangular Norms 339
1 Introduction 339
2 k-Lipschitz t-Norms 341
3 Boundaries of the Class of k-lp-Lipschitz t-Norms 343
4 Transformations of k-Lipschitz t-Norms 349
Acknowledgment 351
References 351
Plenary Talk 353
Formal Models of Knowledge Operators: Rough- Set- Style and Fuzzy- Set- Style Approaches 353
References 353
Invited Session: Looking at Language with Fuzzy Logic 355
Using a Fuzzy Model for Combining Search Results from Di . erent Information Sources to Build a Metasearch Engine 355
1 Introduction 355
2 Foundations 356
3 Metasearch 358
4 Design and Implementation 359
5 Conclusion 362
Acknowledgment 364
References 364
Some Fuzzy Counterparts of the Language uses of And and Or 365
1 Introduction 365
2 Standard Models of And (Or) in Fuzzy Logic 368
3 Relations Induced by an Operation 370
4 Conjunction and Weak Conjunction 370
5 Inclusive or: Disjunction and Weak Disjunction 374
6 Exclusive or: Symmetric Di.erence 377
7 Conclusions 380
Acknowledgment 381
References 381
Fuzzy Sets Versus Language 383
1 Introduction 383
2 On General Theories of Fuzzy Sets 385
3 Decomposable Theories of Fuzzy Sets 386
4 Examples Suggesting a Generalization of the Theories ( T, S, N) 390
5 Antonyms 393
6 Last Comments 395
Acknowledgment 396
References 396
Theory II 397
Some Properties of Fuzzy Languages 397
1 Introduction 397
2 Fuzzy Chomsky Languages 398
3 Fuzzy Petri Net Languages 400
4 Fuzzy Lindenmayer Languages 402
5 Closing Remarks 403
References 403
General Form of Lattice Valued Intuitionistic Fuzzy Sets 405
1 Introduction 405
2 Results 407
Acknowledgement 410
References 411
A Note on Generated Pseudo-Operations with Two Parameters as a base for the Generalized Pseudo- Laplace Type Transform 413
1 Introduction 413
2 Preliminary Notions 414
3 The Generalized (,)-Laplace Transform Based onGenerated Pseudo-Operations with Two Parameters 416
4 Pseudo-Aggregation Operators Based on theGeneralized (,)-Laplace Transforms 421
5 Conclusion 423
Acknowledgments 423
References 423
Theory III 425
Fuzzy All-Pairs Shortest Paths Problem 425
1 Introduction 425
2 Crisp Problem and Its Time Complexity 426
3 Fuzzy Version of the APSPP 431
4 Conclusions 433
Acknowledgement 434
References 434
Optimal Toll Charges in a Fuzzy Flow Problem 435
1 Introduction 435
2 The Fuzzy Flow Problem 436
3 The Toll Finding Problem and Its Reformulation 437
4 Solution Algorithm for the Bilevel Programming Problem 439
5 Conclusion 442
References 442
Modified Interval Global Weights in AHP 445
1 Introduction 445
2 Interval Priority Weights from Crisp Pairwise Comparisons 446
3 Numerical Example 451
4 Conclusion 453
References 454
Plenary Talk 455
Fuzzy Approaches to Trust Management 455
1 Introduction 455
2 Trust Management Systems 456
3 Trust Negotiation Protocols 457
4 Reputation-Based Protocols 458
5 Aggregation-Based Methods for Computing Trust 459
6 Fuzzy Rule-Based Methods for Trust Management 463
7 Conclusions 463
Acknowledgments 464
References 464
Invited Session: Complex-Valued Neural Networks 467
Proposal of Holographic 3D-Movie Generation Using Coherent Neural- Network Interpolation 467
1 Introduction 467
2 Hologram Interpolation Utilizing Generalization 467
3 Simulation Experiment 468
4 Summary 468
References 468
Blur Identification Using Neural Network for Image Restoration 471
1 Introduction 471
2 Image Restoration Problem 473
3 Multilayer Neural Network Based On Multi-Valued Neurons 474
4 Simulations 478
5 Conclusions 483
Acknowledgment 483
References 483
Solving the Parity n Problem and Other Nonlinearly Separable Problems Using a Single Universal Binary Neuron 487
1 Introduction 487
2 UBN and MVN 488
3 Solving the Parity n Problem Using a Single UBN 495
4 Implementation of the Edge Detecting Boolean Functions 499
4 Conclusions 500
References 500
Some Novel Real/Complex-Valued Neural Network Models 503
1 Introduction 503
2 Continuous Time Perceptron and Generalizations 504
3 A New Mathematical Model of Neuron/Single Perceptron 505
4 Abstract Mathematical Structure of Neuronal Models 506
5 Finite Impulse Response Model of Synapses: Neural Networks 508
6 Novel Continuous Time Associative Memory 509
7 Multi-Dimensional Generalizations 511
8 Generalization to Complex-Valued Neural Networks 512
9 Conclusions 512
References 513
Theory IV 515
Extending the Fuzzy Rule Interpolation “ FIVE” by Fuzzy Observation 515
1 Introduction 516
2 The concept of Vague Environment 517
3 Approximate Scaling Function 519
4 Shepard Interpolation for Fuzzy Reasoning: “FIVE” 520
5 Fuzzy Observation by Merging Vague Environments 522
6 Example 524
7 Conclusions 525
Acknowledgement 526
References 526
Fuzzy Rule Interpolation Based on Polar Cuts 529
1 A Brief Overview of Fuzzy Rule Interpolation Methods 530
2 The Structure of the Proposed Method 530
3 Fuzzy Set Interpolation Based on Linguistic Term Shifting and Polar Cuts 531
4 The Position of the Consequent Sets 534
5 Single Rule Reasoning Based on Polar Cuts 535
6 Numerical Examples 538
7 Conclusions 539
8 Acknowledgments 539
References 540
Approximate Reasoning Using Fodor’s Implication 543
1 Introduction 543
2 Basic Concepts 544
3 Generalized Modus Ponens with Fodor’s Implication 545
References 549
Plenary Talk 551
Brain-, Gene-, and Quantum-Inspired Computational Intelligence: Challenges and Opportunities 551
1 Introduction: Brain, Gene, and Quantum Levels of Information Processing in the Brain as Inspirations for ANN and CI Models 552
2 Some Brain-Inspired ECOS Models 553
3 Brain–Gene-Inspired CNGM 559
4 Quantum-Inspired Evolving Connectionist Models 563
5 Conclusions and Directions for Further Research 569
Acknowledgement 569
References 570
Invited Session: Intelligent Data Mining 575
Incremental Learning for E-mail Classification 575
1 Introduction 575
2 Incremental Learning 576
3 Partial Memory Incremental Learning Algorithm FLORA2 577
4 Experiments 580
5 Conclusions 582
References 583
Reduction of Search Space for Instance-Based Classifier Combination 585
1 Introduction 585
2 Reduction of Search Space via Data Condensation 586
3 Adaptive Classi.er Combination 587
4 Case Study: Credit Scoring Data Set 588
5 Conclusions 589
Acknowledgement 590
References 590
Invited Session: Preferences and Decisions 591
Linguistic Matrix Aggregation Operators: Extensions of the Borda Rule 591
1 Introduction 591
2 Extending the Classic Borda Rule to a Linguistic Framework 593
3 Linguistic Matrix Aggregation Operators and Decision Rules 596
4 Social Choice Type Properties 600
5 Some Further Extensions and Concluding Remarks 602
Acknowledgments 603
References 603
Evolutionary Algorithms 607
An Evolutionary Algorithm for the Biobjective QAP 607
1 Introduction 607
2 The EC-Memory Method 608
3 The New Algorithm 610
4 Experimental Results 612
5 Summary 615
Acknowledgements 615
References 615
On a Hill-Climbing Algorithm with Adaptive Step Size: Towards a Control Parameter- Less Black- Box Optimisation Algorithm 617
1 Introduction 617
2 Self-Adaptive Step-size Search (SASS) 618
3 Experiments 618
4 Experimental Results 620
5 Analysis of the SASS Algorithm 620
6 Conclusions and Future Work 624
References 625
Self-Adaptive Baldwinian Search in Hybrid Genetic Algorithms 627
1 Introduction 627
2 Evolutionary Self-Adaptation and Duration of Local Search 628
3 Experiments 629
4 Discussion 630
5 Conclusions 631
References 631
Intragenerational Mutation Shape Adaptation 633
1 Introduction 633
2 The DCMA-ES Algorithm 634
3 Experimental Results 638
4 Conclusions 642
References 642
Theory V 645
The Choquet-Integral as an Aggregation Operator in Case- Based Learning 645
1 Introduction 645
2 Nearest Neighbor Estimation 646
3 The Cho-k-NN Method 647
4 Empirical Validation 651
5 Speci.cation of Similarity Measures 653
6 Concluding Remarks 655
References 656
Fuzzy Sets and Multicriteria Decision Making 659
1 Introduction 659
2 Fuzzy Measures/Aggregation Approach 660
3 Fuzzy Logic Based Construction of Preference Relations 661
4 Preference Relations Based on Orderings of Fuzzy Quantities 662
5 Conclusion 663
Acknowledgment 664
References 664
Fuzzy Reinforcement Learning for Routing in Wireless Sensor Networks 667
1 Introduction 667
2 Assumptions and Problem Formulation 668
3 Fuzzy Reinforcement Learning for Routing in Wireless Sensor Networks 669
4 Experimental Results 673
5 Conclusion 673
References 674
Outlier Resistant Recursive Fuzzy Clustering Algorithms 677
1 Introduction 677
2 Recursive Fuzzy Clustering Algorithm 678
3 Experiments 679
4 Conclusion 681
References 681
Invited Session: Fuzzy Sets – 40 years after 683
Fuzzy Set Theory – 40 Years of Foundational Discussions 683
1 Introduction 683
2 Model Oriented Constructions 684
3 Axiomatizations 688
4 Category Theoretic Approaches 689
References 693
Fuzzy Control – Expectations, Current State, and Perspectives 697
1 Success of Fuzzy Control 698
2 General Problems 701
3 Specific Problems 702
4 Conclusions and Perspectives 704
Acknowledgments 704
References 704
Fuzzy Sets in Categories of Sets with Similarity Relations 707
1 Introduction 707
2 Fuzzy Sets in -sets 708
3 Properties of functors 711
References 712
Fuzzy Sets as a Special Mathematical Model of Vagueness Phenomenon 713
1 Introduction 713
2 Uncertainty and Vagueness 714
3 Actuality and Potentiality 715
4 Fuzzy Sets Naturally Emerge as a Graded Model of Vagueness 716
5 Future Development of Fuzzy Set Theory 718
6 Conclusion 719
References 719
Fuzzy IF-THEN Rules from Logical Point of View 721
1 Introduction 721
2 Special Theory of Fuzzy IF-THEN Rules 724
3 Conclusion 727
References 727
Applications III 683
Synthesizing Adaptive Navigational Robot Behaviours Using a Hybrid Fuzzy A* Approach 729
1 Introduction 729
2 General System Architecture (Fig. 1) 730
3 The Evasion Algorithm 731
4 Cascade of Fuzzy Systems 736
5 Conclusions 739
References 739
Fuzzy Impulse Noise Reduction Methods for Color Images 741
1 Introduction 741
2 Filters for Noise Reduction 742
3 Comparative Study 744
4 Conclusion 749
References 749
Use of Variable Fuzzy Sets Methods for Desertification Evaluation 751
1 Introduction 751
2 Principle of VFS 752
3 VFS for Comprehensive Evaluation of the Deserti . cation Degree 754
4 Conclusion 759
Acknowledgments 760
References 760
A Fuzzy Ultrasonic System for Estimating Degradation of Insulating Oil 763
1 Introduction 763
2 Preliminaries 764
3 Fuzzy Ultrasonic Estimation System 765
4 Experimental Results 769
5 Conclusions 769
References 770
A Genetic Algorithm-Based Fuzzy Inference System in Prediction of Wave Parameters 771
1 Introduction 771
2 Fuzzy Inference Systems (FISs) 772
3 Subtractive Clustering 774
4 Hybrid GA-ANFIS Model 776
5 Application 777
6 Summary and Conclusions 779
References 779
Poster Contributions 781
Estimation of Degree of Polymerisation and Residual Age of Transformers Based on Furfural Levels in Insulating Oil Through Generalized Regression Neural Networks 781
1 Introduction 781
2 Transformer Insulation Measurement and Residual Life Assessment 782
3 Choice of Arti.cial Neural Networks 782
4 Application of Generalized Regression Neural Networks 783
5 Conclusion 785
Acknowledgement 786
References 786
Fuzzy Shortest Paths in Fuzzy Graphs 787
1 Introduction 787
2 Preliminaries 788
3 The Proposed Method 789
4 The Proposed Algorithm 792
5 Simulation 793
6 Conclusion 794
References 794
Improving Vegas Algorithm Using PID and Fuzzy PID Controllers 795
1 Introduction 795
2 Congestion Control 795
3 TCP Vegas 796
4 Developing TCP Vegas using PID Controller 797
5 Developing TCP Vegas using Fuzzy PID Controller 797
6 Performance Evaluation 800
7 Conclusion 804
8 Acknowledgment 805
References 805
A Fuzzy-Based Automation Level Analysis in Irrigation Equipment 807
1 Introduction 807
2 Automation Level and Automation Threshold 808
3 Automation Level Determination 808
4 Energy Resources 809
5 Field 810
6 Mechanization 813
7 Fuzzy Analyzer 813
8 Simulation Results 815
9 Conclusion 816
References 817
Motorized Skateboard Stabilization Using Fuzzy Controller 819
1 Introduction 819
2 Skateboard Model 820
3 Body Model 821
4 Signal processor 822
5 Fuzzy Tuner 823
6 Simulation Results 825
7 Conclusion 827
References 828
Index 831

Textauszug

Fuzzy Control – Expectations, Current State, and Perspectives (p. 667)

Mirko Navara and Milan Petr´ýk

Summary.

We summarize the history of fuzzy sets. We try to find the reasons why fuzzy control has been so successful in applications. This is mainly explained by the fact that fuzzy logic created an alternative to exact computation and it better fits to the human way of reasoning.

We point out some aspects in which current fuzzy systems are not completely satisfactory and directions in which they should develop in the future.

Key words:

Fuzzy set, Fuzzy control, Computational complexity, Fuzzy arithmetic, Stability.

The idea of partial truth and partial membership is old and it has been rediscovered many times (e.g., (4, 7, 13)). However, the seminal paper (28) has opened a new epoch of its rapid development. Our first question is why exactly this work initiated a revolution if many theoretical results (see (4, 24)) have been derived before and remained almost unnoticed.

One reason is that Zadeh expressed this idea in a way accepted by experts in many fields, not only theoretical, but also applied, even by engineers. The preceding papers were recognized only by a limited community of mathematicians. Now the principle was expressed in a way understandable to everybody and in a context drawing new horizons and capabilities of the new technology based on it. It might have been crucial that the applications in control theory followed very soon (14, 26, 29).

Their success ensures permanent interest of industrial partners and financial support of this field. The second reason of success of fuzzy logic in Zadeh’s approach is the state of control theory in the sixties. Preceding development of computers and cybernetics has brought ambitious expectations which have been satisfied only partially. The rapid development of control theory, as initiated by Wiener, has slowed down.

It solved successfully some problems, in particular in control of linear systems, but it has encountered di.culties in control of systems with high non-linearity. These were partially solved by the developing non-linear control theory and by adaptive control, but this efort has brought much more complex questions without a clear trend to their satisfactory solutions. We bring arguments that in some sense the same happened to fuzzy control a few decades later.

The third reason is a disillusion from the limits of computational power. At the first moment, people were fascinated by the newly open possibility of cheap high-precision computations ofered by computers. However, they recognized soon that some solutions are far from satisfactory. Simplified models failed to describe important features of real systems and the solutions did not perform well on some real-world systems.

Then it was found out that supreme precision is not as important. Instead of that, we need to describe (at least roughly) the complexity of the surrounding world. This requires a representation of numerous relations which are not precisely known, but whose effect is at least intuitively understood by humans. Fuzzy logic offered a tool allowing to implement these ideas easily.

Produkt-Details

• Erscheint lt. Verlag: 9.9.2006
• Reihe/Serie: Advances in Intelligent and Soft Computing
• Reihe/Serie: Advances in Intelligent and Soft Computing
• Zusatzinfo: XXX, 802 p. 216 illus., 1 illus. in color.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Technik
• Schlagworte: algorithm • algorithms • Computational Intelligence • Data Mining • Evolution • evolutionary algorithm • Fuzziness • fuzzy • Fuzzy Logic • fuzzy system • Intelligence • learning • machine learning • Modeling • Modelling • neural network • Soft Computing
• ISBN-10: 3-540-34783-6 / 3540347836
• ISBN-13: 978-3-540-34783-5 / 9783540347835