Fuzzy Logic and Soft Computing

CONTENTS......Page 8
PREFACE......Page 6
FUZZY LOGIC AND GENETIC ALGORITHMS......Page 12
1 Evolutionary Algorithms......Page 14
1.1 Genetic Algorithms......Page 15
1.2 Evolution Strategies......Page 16
2 Evolutionary Algorithms for Fuzzy Logic......Page 17
2.1 Optimization of Membership Functions......Page 18
3 Conclusions......Page 19
References......Page 20
1. Introduction......Page 22
3. Genetic Algorithms......Page 23
4. Fuzzy Rule Generating Process......Page 24
4.1.1. Representation......Page 25
4.1.3. Evaluation of individual fitness......Page 26
4.1.4. Genetic Operators......Page 28
4.2. Covering method......Page 29
REFERENCES......Page 30
1. Introduction......Page 32
2. Automatic Design of a Fuzzy System......Page 33
3.2. The generation of a representative by means of mutation......Page 34
3.3. Producing a representative by means of crossing-over......Page 35
4. Bit-string representation......Page 36
5. Example......Page 37
6. Conclusion......Page 38
REFERENCES......Page 39
LEARNING......Page 40
1. Introduction......Page 42
2. Formulation of the problem......Page 43
3. Weights associated with the attributes......Page 45
4. Algorithm......Page 46
REFERENCES......Page 47
1. Introduction......Page 48
2. Outline of the connectionst inference engine......Page 49
3.1. Truth values over temporal intervals......Page 51
4. Knowledge representation and search strategy......Page 52
5. Logical mechanism......Page 55
6. Conclusion......Page 56
1 Introduction......Page 58
2 Discussion of the problem......Page 59
3 The Identification procedure......Page 60
3.2 Net topology......Page 61
4.1 Training the network.......Page 62
4.2 Obtaining the system based on rules.......Page 63
REFERENCES......Page 64
2. Design Concepts of FLINS......Page 65
2.2 Fuzzy Centered Architecture......Page 66
3.1 Fuzzy Case-Based Reasoning......Page 67
3.2.1 Defining Analogy-Based Reasoning(ABR) by an Example......Page 68
3.2.2 Treatment of Fuzziness in Predicates......Page 69
4.2 Handling Misinterpretations Between a System and a User......Page 70
5.3 Studies......Page 71
6. Conclusion......Page 72
REFERENCES......Page 73
2.1. Fuzziness of Fuzzy Set......Page 74
Equilibrium E: Degree of Positive/Negative Belief......Page 75
2.4. Calculation Flow......Page 76
Max-based combination function......Page 78
Probability-based combination......Page 79
Function unit......Page 80
5.2. Examples of the Tuning Process......Page 81
References......Page 83
FUZZY AND HYBRID SYSTEMS......Page 84
1 Introduction......Page 86
2 Autonomous fuzzy intelligent system architecture......Page 87
3 General organization......Page 88
4 Multi-domain intelligent image processing environment......Page 90
4.1 Architecture......Page 91
5 Integrated system structure......Page 92
References......Page 93
1. Introduction......Page 95
3.1. Creating a fine grained fuzzy partition......Page 96
3.3. Partitioning based on decision tree splits......Page 97
4. Pruning and rule generation......Page 98
6. Results......Page 99
7. Conclusions......Page 100
Acknowledgements:......Page 102
REFERENCES......Page 103
1. Introduction......Page 104
2.1 Class I: FNF's of Connectives Corresponding to Pseudo t-norms and conorms......Page 105
2.2 Class II: FNF's of Connectives Corresponding to t-norms and Co-norms......Page 106
2.3 Class III: FNF's of Zadeh's Connectives......Page 107
3.1 Excluded Middle for Zadeh Class......Page 108
3.2. Excluded Middle for t-norm-conorm class.......Page 109
4. Semantic Uncertainty of Type II Fuzzy Sets......Page 110
4.1. Specific Cases of Implication......Page 111
5. Conclusions......Page 112
REFERENCES......Page 113
1. Introduction......Page 114
2.1. Aggregative logic neurons......Page 115
2.2. Referential logic-based neurons......Page 116
3.1. Rule-induced topologies of the networks......Page 117
3.2. Learning......Page 118
3.3. Rules induction......Page 119
4. Representing and processing uncertainty in fuzzy neural networks......Page 120
6. References......Page 121
2.Reference analytical approach......Page 122
3.2 Criterion formulation in fuzzy logic......Page 124
3.3 Fuzzy reasoning applied......Page 125
4.2 Practical introduction of fuzzy logic......Page 126
4.4 Learning the conclusions......Page 127
4.5 Simulations......Page 128
REFERENCES......Page 129
1. Introduction......Page 130
3. The additive connectives in Linear logic......Page 131
3.2. Internal choice......Page 132
3.4. Conclusion......Page 133
4.2. Pseudo firing......Page 134
4.3. Recovery......Page 135
5.1. Description......Page 136
5.2. The disjunctive set of firing sequences......Page 137
Conclusion......Page 138
REFERENCES......Page 139
1. Introduction......Page 140
3. Fuzzy Production Rules and the HLFPN Model......Page 141
4. Backward Reasoning Algorithm......Page 142
REFERENCES......Page 146
1.2. Fuzzy control and neural network control......Page 148
1.4. Universal approximation property for plants with finitely many parameters......Page 149
2.1. Fuzzy control can take only finitely many inputs......Page 150
2.3. Distributed systems and their approximations : formal description......Page 151
3.1. Details of the mathematical construction......Page 152
3.2. How to guarantee that the resulting function is an e — approximation to J......Page 153
4.1. Fuzzy systems with Gaussian membership functions......Page 154
Acknowledgments......Page 155
REFERENCES......Page 156
1. Introduction......Page 157
2. Dealing with non-precise inputs......Page 158
3. Fuzzy triangular inputs......Page 160
4. Different shapes of fuzzy input......Page 162
REFERENCES......Page 164
DECISION AND AGGREGATION TECHNIQUES......Page 166
2. Decision Making With Dispositions......Page 168
3. Immediate Probabilities......Page 171
4. Immediate Probabilities and Allais Paradox......Page 174
5. References......Page 175
1.1 OWA operators......Page 177
2.1 Hierarchical aggregations......Page 178
3 On the degrees of Orness and Dispersion......Page 179
4.1 Dispersion......Page 180
4.2 Orness......Page 181
References......Page 182
1. Introduction......Page 184
2.1. Linguistic assessments......Page 185
2.2. Combination of linguistic values......Page 187
3.1. The collective linguistic preference relation......Page 188
3.2. The linguistic choice process......Page 189
Conclusion......Page 190
REFERENCES......Page 191
1. Introduction......Page 192
2.3. Evaluation of the consensus degree and shifting of positions......Page 193
The Consensus Module (CM)......Page 194
The Source Control System fSCS^)......Page 195
4. Description of a session......Page 196
5. Conclusions......Page 198
REFERENCES......Page 199
2. Definitions......Page 200
3. Main results......Page 201
REFERENCES......Page 204
1. Introduction......Page 205
2. Ordered weighted averaging aggregation operators (OWA)......Page 206
3. Characterization of the OWA aggregator......Page 208
5. Weighted maximum and minimum......Page 209
7. Conclusion......Page 211
REFERENCES......Page 212
1. Utility and preference based decision making......Page 213
2. Outranking approach based on the universal preference function......Page 216
REFERENCES:......Page 219
1. Introduction......Page 220
2. Fuzzy Binary relations and fundamental definitions......Page 221
3.2. Extension of the transitivity property......Page 223
4. Fuzzy covering relations and their properties......Page 225
5. Conclusion......Page 228
REFERENCES......Page 229
1. Introduction......Page 230
2. The numeric to linguistic conversion......Page 231
3. The fuzzy numeric-symbolic conversion......Page 232
4. Rule based symbolic aggregation......Page 233
5. Rule based fuzzy sensor aggregation......Page 234
6. Multi-component numeric-symbolic conversion......Page 236
REFERENCES......Page 238
1. Introduction......Page 239
2.1. Simple additive fuzzy clustering model......Page 240
2.3. Ordinal additive fuzzy clustering model......Page 241
4.1 Simple additive fuzzy clustering model for asymmetric similarity......Page 242
5. Numerical example......Page 243
6. Conclusion......Page 247
References......Page 248
FUZZY LOGIC IN DATABASES......Page 250
1 Introduction......Page 252
2 Initial definitions and notation......Page 253
3 Some reflections about the quotient in classical relational databases......Page 254
4 The fuzzy quotient in FRDBs......Page 256
5 The use of linguistic quantifiers......Page 258
REFERENCES......Page 261
1. Introduction......Page 262
3. Some derived expressions......Page 263
3.2. Complex predicates......Page 264
4.2. General rules for the means......Page 265
4.3.1. The geometric mean......Page 266
4.3.3. The Ordered Weighted Averaging operator (OWA)......Page 267
5.2. Variations according to the connector and the number of predicates......Page 268
5.3. Influence of the selectivity......Page 269
REFERENCES......Page 270
Introduction......Page 272
1.2 Domains......Page 273
2 Identification Process in FIRMS......Page 276
3 Example......Page 278
3.1 First profile......Page 279
References......Page 280
1. Introduction......Page 282
3. Chosen approach......Page 283
4.2. Imperfection of values......Page 284
4.4. Semantical links......Page 285
4.6. Temporal and historic data......Page 286
5.2. Interface classes......Page 287
5.5. Manipulation of real numbers......Page 288
6. Principles of implementation......Page 289
Bibliographie......Page 290
FOUNDATIONS OF FUZZY LOGIC......Page 292
1. Introduction.......Page 294
2. Preliminaries.......Page 295
3. Fuzzy Betweenness relations.......Page 296
4. Dimension and cardinality of betweenness relations.......Page 299
REFERENCES......Page 301
1. Preliminaries.......Page 302
2. Duality......Page 304
3. Duality and T-indistinguishability.......Page 305
4. Natural T-indistinguishabilities and CRI......Page 308
Summary.......Page 309
REFERENCES......Page 310
1. Introduction......Page 311
2.3. Conditioning lower and upper probabilities......Page 313
3.2. Conditioning upper and lower possibility measures: adapting the Moral-Campos' method......Page 315
3.3. Conditioning by constraining the evidential set......Page 316
4.1. Similarities in Product Spaces......Page 317
4.2. Conditioning fuzzy variables in product spaces......Page 318
REFERENCES......Page 319
1. Introduction......Page 321
2. Approximative representation of vaguely defined objects......Page 322
3. Equipotencies between vaguely defined objects......Page 324
4. Generalized cardinal numbers......Page 325
5. Inequalities......Page 327
6. Arithmetic operations......Page 328
REFERENCES......Page 330
1. Introduction......Page 331
2. Structure of Inv(R)......Page 332
3. Lyapunov stability......Page 334
5. Proof of Theorem......Page 336
6. Examples......Page 339
References......Page 340
2. Orderings......Page 341
3. Fuzziness measure and fuzzy measure......Page 343
4. Fuzziness measure via Sugeno's integral......Page 344
5. Homogeneous fuzziness measures......Page 345
6. A representation theorem......Page 346
REFERENCES......Page 347
2.1 Fuzzy quantified statements......Page 348
2.2 Sugeno integrals and increasing quantifiers......Page 349
3.2 Monotonic quantifiers......Page 351
4.1 The algorithm and its heuristics......Page 352
4.2 Use for database fuzzy querying......Page 353
5. Conclusion......Page 354
REFERENCES......Page 355
1. Introduction......Page 356
2. Fuzzy sets and difference posets......Page 357
3. Full difference posets......Page 360
4. Observables and states on fuzzy difference posets......Page 361
References......Page 362
1. Preliminaries......Page 364
2. Basic Properties......Page 365
3. Compositive Measures......Page 366
4. Type-inf composition law......Page 367
5. Type-M composition law......Page 369
References......Page 370
2. Limits of FST......Page 371
3. Utilisation of FST in AI......Page 374
4. Conceptual sets......Page 375
4. 2. Calculation of typicality......Page 376
5. Conclusions......Page 377
REFERENCES......Page 378
APPLICATIONS OF FUZZY SETS......Page 380
1. Introduction......Page 382
2. Event detection and classification......Page 383
3. Time as a fuzzy context......Page 384
4. Episode detection......Page 385
4.1 Fuzzy Temporal Constraint Networks......Page 386
5. Conclusion and Discussion......Page 388
REFERENCES......Page 389
1. Introduction......Page 390
3.1 Representation of clinical signs......Page 391
4. The neural stage......Page 392
4.1 Problem dependent learning rule in feed-forward neural networks......Page 393
4.2. Neural network implementation......Page 395
REFERENCES......Page 396
2.1. Decision Engine......Page 397
2.2. Fuzzy Inference......Page 398
3. Decision Graph......Page 399
4.1. Inferences about decisions......Page 401
4.2. Associations of decisions......Page 402
5. AntibES : an Antibiotic Expert System......Page 403
REFERENCES......Page 404
1 Introduction......Page 405
2.1.Image content representation......Page 406
2.2.Querying an image database......Page 407
2.4.Query representation......Page 408
3 Description of the retrieval procedure......Page 409
3.1.Elementary compatibility......Page 410
3.2.Intermediate and global compatibility......Page 411
4 Results......Page 412
5 Conclusion......Page 413
REFERENCES......Page 414
1. Introduction......Page 415
2. The idea of multivalued segmentation......Page 416
3.2. Pixel labelling......Page 417
5. Conclusion......Page 418
REFERENCES......Page 421
1 Introduction......Page 422
2 Glucose regulation......Page 423
3 Why a fuzzy model ?......Page 424
4 Fuzzy modelization......Page 425
5 Constrained supervised learning......Page 426
6 Work in progress......Page 428
References......Page 429
2.1. Network Design......Page 432
2.3. Fuzzy Aspects of Network......Page 433
3.3 Interpretation of Symbolic Layer......Page 434
4.2. Crisp Implementation......Page 435
4.3. Symbolic Layer......Page 436
5. Conclusion......Page 437
REFERENCES......Page 438
2. Comprehensive evaluation......Page 439
3. Fuzzy multi-level comprehensive evaluation......Page 440
3.2 Economic (cost-benefit) evaluation......Page 442
3.4 Environmental impact evaluation......Page 443
REFERENCES......Page 444
1. INTRODUCTION......Page 445
2. CONSTRAINTS......Page 446
3. DESIGN......Page 447
4. FUZZY STRATEGY......Page 448
5.1 The prototype......Page 449
5.2 Real tests......Page 450
6. CONCLUSIONS AND PERSPECTIVES......Page 451
REFERENCES......Page 452
I - Introduction......Page 455
II - The concept of posture comfort......Page 456
IV. 1 - Description of the command system - Design constraints......Page 457
IV.3 - Quantifying the knowledge base......Page 458
V - Results......Page 460
VI. Summary and conclusion......Page 461
References......Page 462
2. Multiple Attribute Fuzzy Decision Support System Overview......Page 463
3. Heroes of Ancient Mythology......Page 466
4. Military Vehicle Recognition......Page 469
References......Page 472
SPECIAL INVITED PAPER......Page 474
1. Introduction: Converting Variant and Noisy Data into Invariant Recognition Codes......Page 476
2. The Seibert-Waxman Architecture......Page 477
3. Overview of VIEWNET 1......Page 479
4. Airplane Data Base......Page 481
5. CORT-X 2 Filter......Page 482
6. Translation, Rotation and Scale Invariance......Page 486
7. Coarse Coding......Page 488
8. Learning Recognition Categories Using Fuzzy ARTMAP......Page 490
9. Illustrative Simulation Results......Page 493
Fast Learning With and Without Noise......Page 495
Slow Learning Simulation With Noise......Page 497
10. Evidence Accumulation by Voting and View Transitions......Page 499
11. Concluding Remarks......Page 501
Appendix A: CORT-X 2 Equations......Page 502
Appendix B: Fuzzy ARTMAP Equations......Page 505
REFERENCES......Page 507