Fuzzy Sets and Fuzzy Logic: Theory and Applications

Dedication......Page 4
Contents......Page 6
Foreword......Page 12
Preface......Page 14
1.1 Introduction......Page 18
1.2 Crisp Sets: An Overview......Page 22
1.3 Fuzzy Sets: Basic Types......Page 28
1.4 Fuzzy Sets: Basic Concepts......Page 36
1.5 Characteristics and Significance of the Paradigm Shift......Page 47
Notes......Page 49
Exercises......Page 50
2.1 Additional Properties of α-Cuts......Page 52
2.2 Representations of Fuzzy Sets......Page 56
2.3 Extension Principle for Fuzzy Sets......Page 61
Notes......Page 65
Exercises......Page 66
3.1 Types of Operations......Page 67
3.2 Fuzzy Complements......Page 68
3.3 Fuzzy Intersections: t-Norms......Page 78
3.4 Fuzzy Unions: t-Conorms......Page 93
3.5 Combinations of Operations......Page 100
3.6 Aggregation Operations......Page 105
Notes......Page 111
Exercises......Page 112
4.1 Fuzzy Numbers......Page 114
4.3 Arithmetic Operations on Intervals......Page 119
4.4 Arithmetic Operations on Fuzzy Numbers......Page 122
4.5 Lattice of Fuzzy Numbers......Page 126
4.6 Fuzzy Equations......Page 131
Exercises......Page 134
5.1 Crisp and Fuzzy Relations......Page 136
5.2 Projections and Cylindric Extensions......Page 139
5.3 Binary Fuzzy Relations......Page 141
5.4 Binary Relations on a Single Set......Page 145
5.5 Fuzzy Equivalence Relations......Page 149
5.6 Fuzzy Compatibility Relations......Page 152
5.7 Fuzzy Ordering Relations......Page 154
5.8 Fuzzy Morphisms......Page 158
5.9 Sup-i Compositions of Fuzzy Relations......Page 161
5.10 Inf-ω i Compositions of Fuzzy Relations......Page 163
Exercises......Page 166
6.1 General Discussion......Page 170
6.2 Problem Partitioning......Page 171
6.3 Solution Method......Page 173
6.3 Fuzzy Relation Equations Based on Sup-i Compositions......Page 179
6.5 Fuzzy Relation Equations Based on Inf-ω i Compositions......Page 181
6.6 Approximate Solutions......Page 183
6.7 The Use of Neural Networks......Page 188
Notes......Page 190
Exercises......Page 192
7.1 Fuzzy Measures......Page 194
7.2 Evidence Theory......Page 197
7.3 Possibility Theory......Page 204
7.4 Fuzzy Sets and Possibility Theory......Page 215
7.5 Possibility Theory versus Probability Theory......Page 217
Notes......Page 225
Exercises......Page 226
8.1 Classical Logic: An Overview......Page 229
8.2 Multivalued Logics......Page 234
8.3 Fuzzy Propositions......Page 237
8.4 Fuzzy Quantifiers......Page 242
8.5 Linguistic Hedges......Page 246
8.6 Inference from Conditional Fuzzy Propositions......Page 248
8.7 Inference from Conditional and Qualified Propositions......Page 253
8.8 Inference from Quantified Propositions......Page 256
Exercises......Page 259
9.1 Information and Uncertainty......Page 262
9.2 Nonspecificity of Crisp Sets......Page 264
9.3 Nonspecificity of Fuzzy Sets......Page 267
9.4 Fuzziness of Fuzzy Sets......Page 271
9.5 Uncertainty in Evidence Theory......Page 275
9.6 Summary of Uncertainty Measures......Page 284
9.7 Principles of Uncertainty......Page 286
Notes......Page 294
Exercises......Page 295
10.1 General Discussion......Page 297
10.2 Methods of Construction: An Overview......Page 298
10.3 Direct Methods with One Expert......Page 299
10.4 Direct Methods with Multiple Experts......Page 300
10.5 Indirect Methods with One Expert......Page 304
10.6 Indirect Methods with Multiple Experts......Page 305
10.7 Constructions from Sample Data......Page 307
Notes......Page 317
Exercises......Page 318
11.1 Fuzzy Expert Systems: An Overview......Page 319
11.2 Fuzzy Implications......Page 321
11.3 Selection of Fuzzy Implications......Page 329
11.4 Multiconditional Approximate Reasoning......Page 334
11.5 The Role of Fuzzy Relation Equations......Page 338
11.6 Interval-Valued Approximate Reasoning......Page 340
Exercises......Page 342
12.1 General Discussion......Page 344
12.2 Fuzzy Controllers: An Overview......Page 347
12.3 Fuzzy Controllers: An Example......Page 356
12.4 Fuzzy Systems and Neural Networks......Page 361
12.5 Fuzzy Neural Networks......Page 364
12.6 Fuzzy Automata......Page 366
12.7 Fuzzy Dynamic Systems......Page 370
Notes......Page 371
Exercises......Page 373
13.1 Introduction......Page 374
13.2 Fuzzy Clustering......Page 375
13.3 Fuzzy Pattern Recognition......Page 382
13.4 Fuzzy Image Processing......Page 391
Notes......Page 394
Exercises......Page 395
14.1 General Discussion......Page 396
14.2 Fuzzy Databases......Page 398
14.3 Fuzzy Information Retrieval......Page 402
Exercises......Page 405
15.1 General Discussion......Page 407
15.2 Individual Decision Making......Page 408
15.3 Multiperson Decision Making......Page 412
15.4 Multicriteria Decision Making......Page 416
15.5 Multistage Decision Making......Page 418
15.6 Fuzzy Ranking Methods......Page 422
15.7 Fuzzy Linear Programming......Page 425
Notes......Page 432
Exercises......Page 433
16.1 Introduction......Page 435
16.2 Civil Engineering......Page 436
16.3 Mechanical Engineering......Page 443
16.4 Industrial Engineering......Page 449
16.5 Computer Engineering......Page 453
16.6 Reliability......Page 456
Notes......Page 457
Exercises......Page 458
17.2 Medicine......Page 460
17.3 Economics......Page 467
17.4 Fuzzy Systems and Genetic Algortihms......Page 469
17.5 Fuzzy Regression......Page 471
17.6 Interpersonal Communication......Page 476
17.7 Other Applications......Page 480
Notes......Page 482
Exercises......Page 483
Appendix A. Artificial Neural Networks: An Overview......Page 484
Appendix B. Genetic Algorithms: An Overview......Page 493
Appendix C. Fuzzy Sets versus Rough Sets......Page 498
D.1 The Proof of Theorem 3.7 (Sec. 3.2, p. 59)......Page 501
D.2 Proof of Theorem 3.13 (Sec. 3.3, p. 75)......Page 502
D.3 Proof of Theorem 3.28 (Sec. 3.6, p. 96)......Page 503
Appendix E. Glossary of Key Concepts......Page 504
General Symbols......Page 507
Special Symbols......Page 509
Bibliography......Page 511
Bibliographical Index......Page 565
Name Index......Page 569
A-B......Page 580
C......Page 581
D-E......Page 582
F......Page 583
G-H-I......Page 584
J-K-L-M......Page 585
N-O......Page 586
P......Page 587
Q-R......Page 588
S......Page 589
T-U-V......Page 590
W-X-Y-Z......Page 591