PARTI：FUNDAMENTALS 1
CHAPTER1. CLASSICAL SETS VERSRS FUZZY SETS 1
1.1 Introduction 1
1.2 Crisp Sets: Terminology and Notation 6
1.3 Basic Concepts of Fuzzy Sets 10
1.4 Representations of Fuzzy Sets 18
1.5 Extension Principle 22
CHAPTER 2. OPERATIONS ON FUZZY SETS 28
2.1 Fuzzy Complements 28
2.2 Fuzzy Intersecions and Unions 31
2.3 Averaging Operations 35
2.4 Arithmetic Oerations on Fuzzy Numbers 40
CHAPTER 3. FUZZY RELATIONS 50
3.1 Basic Concepts of Fuzzy Relations 50
3.2 Fuzzy Relations on a Single Set 57
3.3 Fuzzy Relation Equations 65
CHAPTER 4.FUZZY LOGIC 69
4.1 Fuzzy Set Theory and Fuzzy logic 69
4.2 Components of Fuzzy Logic 71
4.3 Approximate Reasoning 79
4.4 Fuzzy Logic and Possibility Theory 81
PART II: APPLICATIONS 87
CHAPTER 5. CONSTRUCTING FUZZY SETS 87
CHAPTER 6. FUZZY SYSTEMS 90
CHAPTER 7. FUZZY CONTROL 96
CHAPTER 8 CLUSTERING, PATTERN RECOGNITION,AND IMAGE PROCESSING 109
CHAPTER 9. DECISION MAKING 112
CHAPTER 10. FUZZY INFORMATION AND KNOWLEDGEBASED SYSTEMS 116
CHAPTER 11. ENGINEERING APPLICATIONS 121
CHAPTER 12. OTHER APPLICATIONS 125
BIBLIOGRAPHICAL COMMENTS TO PARTS I II 129
BIBLIOGRPHICAL INDEX TO PARTS I II 135
BIBLIOGRAPHY TO PARTS I II 139
PART III. PERSONAL VIEWS 173
CHAPTER 13.SIGNIFICANCE OF FUZZY SET THEORY 173
CHAPTER 14.FROM CLASSICAL SETS TO FUZZY SETS:A Grand Paradigm Shift 180
14.1. Introduction 180
14.2. What are Scientific Paradigms and Paradigrn Shifts 181
14.3. Characteristics of the New Uncertainty Paradigm 182
14.4. The Role of Uncertainty in Science and Technology 186
14.5. Stages in the Paradigm Shift 195
14.6. Significant Issues of Future Research 203
References 205
CHAPTER 15. MULTIVALUED LOGICS VERSUS MODAL LOGICS: Alternative Frameworks for Uncertainty Modelling 209
15.1. Attitudes Towards Uncertainty 209
15.2. Uncertainty Theories 211
15.3. Uncertainty and Multivalued Logics 213
15.4. Modal Logics:An Overview 218
15.5. Uncertainty and Modal Logics 228
15.6. Conclusions 248
References 250
CHAPTER 16.MODAL LOGIC INTERPRETATION OF POSSIBILITY THEORY 256
16.1. Introduction 256
16.2. Basics of Possibility Theory 257
16.3. Basics of Modal Logic 258
16.4. Interpretation of Possibility Theory 260
16.5. Completeness 264
16.6. Conclusions 268
References 268
CHAPTER 17.FUZZY-SET INTERPRETATION OF POSSIBILITY THEORY 270
17.1. Introduction 270
17.2. Possibility Theory 271
17.3 Possibility Theory and Dempster-Shafer Theory 274
17.4 Standard Fuzzy-Set Interpretation of Possibility Theory 276
17.5 The Issue of Subnormal Fuzzy Sets 278
17.6 Revised Fuzzy-Set Interpretation of Possibility Theory 281
17.7. Conclusions 286
References 287
CHAPTER 18. CONSTRAINED FUZZY ARITHMETIC 290
18.1. Introduction 290
18.2. Standard Fuzzy Arithmetic 292
18.3. Constrained Fuzzy Arithmetic 294
18.4. Requisite Equality Constraints 298
18.5. Other Requisite Constraints 302
18.6. Applications of Fuzzy Atithmetic 305
18.7. Conclusions 309
References 310
CHAPTER 19. UNCERTAINTY AND PROBABILITY: A Debate 315
19.1. Introduction: Setting the Stage 315
19.2. What is Uncertainty 317
19.3. Mathematical Frameworks for Conceptualizing Uncertainty 319
19.4. Measures of Uncertainty 326
19.5. Limitatios of Probability Theory 334
19.6. Examples 346
19.7. Comclusions 352
References 354