Reflecting the tremendous advances that have taken place in the study of fuzzy set theory and fuzzy logic from 1988 to the present, this book not only details the theoretical advances in these areas, but considers a broad variety of applications of fuzzy sets and fuzzy logic as well. Theoretical aspects of fuzzy set theory and fuzzy logic are covered in Part I of the text, including: basic types of fuzzy sets; connections between fuzzy sets and crisp sets; the various aggregation operations of fuzzy sets; fuzzy numbers and arithmetic operations on fuzzy numbers; fuzzy relations and the study of fuzzy relation equations. Part II is devoted to applications of fuzzy set theory and fuzzy logic, including: various methods for constructing membership functions of fuzzy sets; the use of fuzzy logic for approximate reasoning in expert systems; fuzzy systems and controllers; fuzzy databases; fuzzy decision making; and engineering applications. For everyone interested in an introduction to fuzzy set theory and fuzzy logic.
Author(s): George J. Klir, Bo Yuan
Edition: 1st
Publisher: Prentice Hall
Year: 1995
Language: English
Pages: 590
FUZZY SETS AND FUZZY LOGIC: THEORY AND APPLICATIONS......Page 1
Title Page......Page 2
Copyright Page......Page 3
Dedication......Page 5
Contents......Page 6
Foreword......Page 12
Preface......Page 14
1.1 Introduction......Page 17
1.2 Crisp Sets: An Overview......Page 21
1.3 Fuzzy Sets: Basic Types......Page 27
1.4 Fuzzy Sets: Basic Concepts......Page 35
1.5 Characteristics and Significance of the Paradigm Shift......Page 46
Notes......Page 48
Exercises......Page 49
2.1 Additional Properties of α-Cuts......Page 51
2.2 Representations of Fuzzy Sets......Page 55
2.3 Extension Principle for Fuzzy Sets......Page 60
Notes......Page 64
Exercises......Page 65
3.1 Types of Operations......Page 66
3.2 Fuzzy Complements......Page 67
3.3 Fuzzy Intersections: t-Norms......Page 77
3.4 Fuzzy Unions: t-Conorms......Page 92
3.5 Combinations of Operations......Page 99
3.6 Aggregation Operations......Page 104
Notes......Page 110
Exercises......Page 111
4.1 Fuzzy Numbers......Page 113
4.3 Arithmetic Operations on Intervals......Page 118
4.4 Arithmetic Operations on Fuzzy Numbers......Page 121
4.5 Lattice of Fuzzy Numbers......Page 125
4.6 Fuzzy Equations......Page 130
Exercises......Page 133
5.1 Crisp and Fuzzy Relations......Page 135
5.2 Projections and Cylindric Extensions......Page 138
5.3 Binary Fuzzy Relations......Page 140
5.4 Binary Relations on a Single Set......Page 144
5.5 Fuzzy Equivalence Relations......Page 148
5.6 Fuzzy Compatibility Relations......Page 151
5.7 Fuzzy Ordering Relations......Page 153
5.8 Fuzzy Morphisms......Page 157
5.9 Sup-i Compositions of Fuzzy Relations......Page 160
5.10 Inf-ω i Compositions of Fuzzy Relations......Page 162
Exercises......Page 165
6.1 General Discussion......Page 169
6.2 Problem Partitioning......Page 170
6.3 Solution Method......Page 172
6.3 Fuzzy Relation Equations Based on Sup-i Compositions......Page 178
6.5 Fuzzy Relation Equations Based on Inf-ω i Compositions......Page 180
6.6 Approximate Solutions......Page 182
6.7 The Use of Neural Networks......Page 187
Notes......Page 189
Exercises......Page 191
7.1 Fuzzy Measures......Page 193
7.2 Evidence Theory......Page 196
7.3 Possibility Theory......Page 203
7.4 Fuzzy Sets and Possibility Theory......Page 214
7.5 Possibility Theory versus Probability Theory......Page 216
Notes......Page 224
Exercises......Page 225
8.1 Classical Logic: An Overview......Page 228
8.2 Multivalued Logics......Page 233
8.3 Fuzzy Propositions......Page 236
8.4 Fuzzy Quantifiers......Page 241
8.5 Linguistic Hedges......Page 245
8.6 Inference from Conditional Fuzzy Propositions......Page 247
8.7 Inference from Conditional and Qualified Propositions......Page 252
8.8 Inference from Quantified Propositions......Page 255
Exercises......Page 258
9.1 Information and Uncertainty......Page 261
9.2 Nonspecificity of Crisp Sets......Page 263
9.3 Nonspecificity of Fuzzy Sets......Page 266
9.4 Fuzziness of Fuzzy Sets......Page 270
9.5 Uncertainty in Evidence Theory......Page 274
9.6 Summary of Uncertainty Measures......Page 283
9.7 Principles of Uncertainty......Page 285
Notes......Page 293
Exercises......Page 294
10.1 General Discussion......Page 296
10.2 Methods of Construction: An Overview......Page 297
10.3 Direct Methods with One Expert......Page 298
10.4 Direct Methods with Multiple Experts......Page 299
10.5 Indirect Methods with One Expert......Page 303
10.6 Indirect Methods with Multiple Experts......Page 304
10.7 Constructions from Sample Data......Page 306
Notes......Page 316
Exercises......Page 317
11.1 Fuzzy Expert Systems: An Overview......Page 318
11.2 Fuzzy Implications......Page 320
11.3 Selection of Fuzzy Implications......Page 328
11.4 Multiconditional Approximate Reasoning......Page 333
11.5 The Role of Fuzzy Relation Equations......Page 337
11.6 Interval-Valued Approximate Reasoning......Page 339
Exercises......Page 341
12.1 General Discussion......Page 343
12.2 Fuzzy Controllers: An Overview......Page 346
12.3 Fuzzy Controllers: An Example......Page 355
12.4 Fuzzy Systems and Neural Networks......Page 360
12.5 Fuzzy Neural Networks......Page 363
12.6 Fuzzy Automata......Page 365
12.7 Fuzzy Dynamic Systems......Page 369
Notes......Page 370
Exercises......Page 372
13.1 Introduction......Page 373
13.2 Fuzzy Clustering......Page 374
13.3 Fuzzy Pattern Recognition......Page 381
13.4 Fuzzy Image Processing......Page 390
Notes......Page 393
Exercises......Page 394
14.1 General Discussion......Page 395
14.2 Fuzzy Databases......Page 397
14.3 Fuzzy Information Retrieval......Page 401
Exercises......Page 404
15.1 General Discussion......Page 406
15.2 Individual Decision Making......Page 407
15.3 Multiperson Decision Making......Page 411
15.4 Multicriteria Decision Making......Page 415
15.5 Multistage Decision Making......Page 417
15.6 Fuzzy Ranking Methods......Page 421
15.7 Fuzzy Linear Programming......Page 424
Notes......Page 431
Exercises......Page 432
16.1 Introduction......Page 434
16.2 Civil Engineering......Page 435
16.3 Mechanical Engineering......Page 442
16.4 Industrial Engineering......Page 448
16.5 Computer Engineering......Page 452
16.6 Reliability......Page 455
Notes......Page 456
Exercises......Page 457
17.2 Medicine......Page 459
17.3 Economics......Page 466
17.4 Fuzzy Systems and Genetic Algortihms......Page 468
17.5 Fuzzy Regression......Page 470
17.6 Interpersonal Communication......Page 475
17.7 Other Applications......Page 479
Notes......Page 481
Exercises......Page 482
Appendix A. Artificial Neural Networks: An Overview......Page 483
Appendix B. Genetic Algorithms: An Overview......Page 492
Appendix C. Fuzzy Sets versus Rough Sets......Page 497
D.1 The Proof of Theorem 3.7 (Sec. 3.2, p. 59)......Page 500
D.2 Proof of Theorem 3.13 (Sec. 3.3, p. 75)......Page 501
D.3 Proof of Theorem 3.28 (Sec. 3.6, p. 96)......Page 502
Appendix E. Glossary of Key Concepts......Page 503
General Symbols......Page 506
Special Symbols......Page 508
Bibliography......Page 510
Bibliographical Index......Page 564
Name Index......Page 568
A-B......Page 579
C......Page 580
D-E......Page 581
F......Page 582
G-H-I......Page 583
J-K-L-M......Page 584
N-O......Page 585
P......Page 586
Q-R......Page 587
S......Page 588
T-U-V......Page 589
W-X-Y-Z......Page 590
