模糊集合论及其应用 第4版 英文PDF电子书下载

1 Introduction to Fuzzy Sets 1

1.1 Crispness, Vagueness, Fuzziness, Uncertainty 1

1.2 Fuzzy Set Theory 2

PartⅠ: Fuzzy Mathematics 9

2 Fuzzy Sets-Basic Definitions 11

2.1 Basic Definitions 11

2.2 Basic Set-Theoretic Operations for Fuzzy Sets 16

3 Extensions 23

3.1 Types of Fuzzy Sets 23

3.2 Further Operations on Fuzzy Sets 27

3.2.1 Algebraic Operations 28

3.2.2 Set-Theoretic Operations 29

3.2.3 Criteria for Selecting Appropriate Aggregation Operators 43

4 Fuzzy Measures and Measures of Fuzziness 47

4.1 Fuzzy Measures 47

4.2 Measures of Fuzziness 49

5 The Extension Principle and Applications 55

5.1 The Extension Principle 55

5.2 Operations for Type 2 Fuzzy Sets 56

5.3 Algebraic Operations with Fuzzy Numbers 59

5.3.1 Special Extended Operations 61

5.3.2 Extended Operations for LR-Representation of Fuzzy Sets 64

6 Fuzzy Relations and Fuzzy Graphs 71

6.1 Fuzzy Relations on Sets and Fuzzy Sets 71

6.1.1 Compositions of Fuzzy Relations 76

6.1.2 Properties of the Min-Max Composition 79

6.2 Fuzzy Graphs 83

6.3 Special Fuzzy Relations 86

7 Fuzzy Analysis 93

7.1 Fuzzy Functions on Fuzzy Sets 93

7.2 Extrema of Fuzzy Functions 95

7.3 Integration of Fuzzy Functions 99

7.3.1 Integration of a Fuzzy Function over a Crisp Interval 100

7.3.2 Integration of a （Crisp） Real-Valued Function over a Fuzzy Interval 103

7.4 Fuzzy Differentiation 107

8 Uncertainty Modeling 111

8.1 Application-oriented Modeling of Uncertainty 111

8.1.1 Causes of Uncertainty 114

8.1.2 Type of Available Information 117

8.1.3 Uncertainty Methods 118

8.1.4 Uncertainty Theories as Transformers of Information 119

8.1.5 Matching Uncertainty Theory and Uncertain Phenomena 120

8.2 Possibility Theory 122

8.2.1 Fuzzy Sets and Possibility Distributions 122

8.2.2 Possibility and Necessity Measures 126

8.3 Probability of Fuzzy Events 129

8.3.1 Probability of a Fuzzy Event as a Scalar 129

8.3.2 Probability of a Fuzzy Event as a Fuzzy Set 131

8.4 Possibility vs.Probability 133

Part I: Applications of Fuzzy Set Theory 139

9 Fuzzy Logic and Approximate Reasoning 141

9.1 Linguistic Variables 141

9.2 Fuzzy Logic 149

9.2.1 Classical Logics Revisited 149

9.2.2 Linguistic Truth Tables 153

9.3 Approximate and Plausible Reasoning 156

9.4 Fuzzy Languages 160

9.5 Support Logic Programming and Fril 169

9.5.1 Introduction 169

9.5.2 Fril Rules 170

9.5.3 Inference Methods in Fril 172

9.5.4 Fril Inference for a Single Rule 175

9.5.5 Multiple Rule Case 176

9.5.6 Interval and Point Semantic Unification 177

9.5.7 Least Prejudiced Distribution and Learning 179

9.5.8 Applications of Fril 181

10 Fuzzy Sets and Expert Systems 185

10.1 Introduction to Expert Systems 185

10.2 Uncertainty Modeling in Expert Systems 193

10.3 Applications 203

11 Fuzzy Control 223

11.1 Origin and Objective 223

11.2 Automatic Control 225

11.3 The Fuzzy Controller 226

11.4 Types of Fuzzy Controllers 228

11.4.1 The Mamdani Controller 228

11.4.2 Defuzzification 232

11.4.3 The Sugeno Controller 239

11.5 Design Parameters 240

11.5.1 Scaling Factors 240

11.5.2 Fuzzy Sets 240

11.5.3 Rules 242

11.6 Adaptive Fuzzy Control 243

11.7 Applications 244

11.7.1 Crane Control 244

11.7.2 Control of a Model Car 246

11.7.3 Control of a Diesel Engine 248

11.7.4 Fuzzy Control of a Cement Kiln 249

11.8 Tools 255

11.9 Stability 257

11.10 Extensions 262

12 Fuzzy Data Bases and Queries 265

12.1 Introduction 265

12.2 Fuzzy Relational Databases 266

12.3 Fuzzy Queries in Crisp Databases 268

13 Fuzzy Data Analysis 277

13.1 Introduction 277

13.2 Methods for Fuzzy Data Analysis 279

13.2.1 Algorithmic Approaches 281

13.2.2 Knowledge-Based Approaches 302

13.2.3 Neural Net Approaches 304

13.3 Dynamic Fuzzy Data Analysis 306

13.3.1 Problem Description 306

13.3.2 Similarity of Functions 307

13.3.3 Approaches for Analysic Dynamic Systems 313

13.4 Tools for Fuzzy Data Analysis 317

13.4.1 Requirements for FDA Tools 317

13.4.2 Data Engine 318

13.5 Applications of FDA 322

13.5.1 Maintenance Management in Petrochemical Plants 322

13.5.2 Acoustic Quality Control 323

14 Decision Making in Fuzzy Environments 329

14.1 Fuzzy Decisions 329

14.2 Fuzzy Linear Programming 336

14.2.1 Symmetric Fuzzy LP 337

14.2.2 Fuzzy LP with Crisp Objective Function 342

14.3 Fuzzy Dynamic Programming 348

14.3.1 Fuzzy Dynamic Programming with Crisp State Transformation Function 349

14.4 Fuzzy Multicriteria Analysis 352

14.4.1 Multi Objective Decision Making （MODM） 353

14.4.2 Multi Attributive Decision Making （MADM） 359

15 Applications of Fuzzy Sets in Engineering and Management 371

15.1 Introduction 371

15.2 Engineering Applications 373

15.2.1 Linguistic Evaluation and Ranking of Machine Tools 375

15.2.2 Fault Detection in Gearboxes 381

15.3 Applications in Management 389

15.3.1 A Discrete Location Model 390

15.3.2 Fuzzy Set Models in Logistics 393

15.3.2.1 Fuzzy Approach to the Transportation Problem 393

15.3.2.2 Fuzzy Linear Programming in Logistics 398

15.3.3 Fuzzy Sets in Scheduling 401

15.3.3.1 Job-Shop Scheduling with Expert Systems 401

15.3.3.2 A Method to Control Flexible Manufacturing Systems 405

15.3.3.3 Aggregate Production and Inventory Planning 411

15.3.3.4 Fuzzy Mathematical Programming for Maintenance Scheduling 418

15.3.3.5 Scheduling Courses, Instructors, and Classrooms 419

15.3.4 Fuzzy Set Models in Inventory Control 426

15.3.5 Fuzzy Sets in Marketing 432

15.3.5.1 Customer Segmentation in Banking and Finance 432

15.3.5.2 Bank Customer Segmentation based on Customer Behavior 433

16 Empirical Research in Fuzzy Set Theory 443

16.1 Formal Theories vs& Factual Theories vs.Decision Technologies 443

16.1.1 Models in Operations Research and Management Science 447

16.1.2 Testing Factual Models 449

16.2 Empirical Research on Membership Functions 453

16.2.1 Type A-Membership Model 454

16.2.2 Type B-Membership Model 456

16.3 Empirical Research on Aggregators 463

16.4 Conclusions 474

17 Future Perspectives 477

Abbreviations of Frequently Cited Journals 481

Bibliography 483

Index 507

Figure 1-1 Concept hierarchy of creditworthiness. 5

Figure 2-1 Real numbers close to 10. 13

Figure 2-2a Convex fuzzy set. 15

Figure 2-2b Nonconvex fuzzy set. 15

Figure 2-3 Union and intersection of fuzzy sets. 18

Figure 3-1 Fuzzy sets vs.probabilistic sets. 26

Figure 3-2 Mapping of t-norms,t-conorms, and averaging operators. 38

Figure 5-1 The extension principle. 57

Figure 5-2 Trapezoidal “fuzzy number”. 60

Figure 5-3 LR representation of fuzzy numbers. 65

Figure 6-1 Fuzzy graphs. 84

Figure 6-2 Fuzzy forests. 86

Figure 6-3 Graphs that are not forests. 86

Figure 7-1 Maximizing set. 96

Figure 7-2 A fuzzy function. 97

Figure 7-3 Triangular fuzzy numbers representing a fuzzy function. 98

Figure 7-4 The maximum of a fuzzy function. 99

Figure 7-5 Fuzzily bounded interval. 104

Figure 8-1 Uncertainty as situational property. 113

Figure 8-2 Probability of a fuzzy event. 134

Figure 9-1 Linguistic variable “Age”. 143

Figure 9-2 Linguistic variable “Probability. 144

Figure 9-3 Linguistic variable “Truth”. 145

Figure 9-4 Terms “True” and “False”. 146

Figure 10-1 Structure of an expert system. 189

Figure 10-2 Semantic net. 191

Figure 10-3 Linguistic descriptors. 205

Figure 10-4 Label sets for semantic representation. 205

Figure 10-5 Linguistic variables for occurrence and confirmability. 209

Figure 10-6 Inference network for damage assessment of existing structures [Ishizuka et al.1982, p.263]. 212

Figure 10-7 Combination of two two-dimensional portfolios. 215

Figure 10-8 Criteria tree for technology attractiveness. 216

Figure 10-9 Terms of “degree of achievement”. 217

Figure 10-10 Aggregation of linguistic variables. 218

Figure 10-11 Portfolio with linguistic input. 220

Figure 10-12 Structure of ESP. 221

Figure 11-1 Automatic feedback control. 225

Figure 11-2 Generic Mamdani fuzzy controller. 227

Figure 11-3 Linguistic variable “Temperature”. 229

Figure 114Rule consequences in the heating system example. 232

Figure 115Extreme Value Strategies. 234

Figure 116COA Defuzzification. 235

Figure 11-7 Neighboring membership functions. 236

Figure 118Separate membership functions. 236

Figure 119Parameters describing fuzzy sets. 241

Figure 11-10 Influence of symmetry. 242

Figure 11-11 Condition width. 242

Figure 11-12 Container crane [von Altrock 1993]. 245

Figure 11-13 Phases of motion. 245

Figure 11-14 Input variables [Sugeno and Nishida 1985, p.106]. 246

Figure 11-15 Trajectories of the fuzzy controlled model car [Sugeno and Nishida 1985, p.112]. 247

Figure 11-16 Fuzzy model car [von Altrock et al.1992, p.42]. 248

Figure 11-17 Experimental design [von Altrock et al.1992, p.48]. 249

Figure 11-18 FCR vs.fuel injection timing [Murayama et al.1985, p.64]. 250

Figure 11-19 Control algorithm [Murayama et al.1985]. 251

Figure 11-20 Experimental results [Murayama et al.1985]. 252

Figure 11-21 Schematic diagram of rotary cement kiln [Umbers andKing 1981，p.371]. 252

Figure 11-22 Controller development in fuzzyTECH [von Altrock et al.1992]. 256

Figure 11-23 Rule base for model car [von Altrock et al.1992]. 256

Figure 11-24 Simulation screen [von Altrock et al.1992]. 257

Figure 11-25 Fuzzy controller as a nonlinear transfer element. 258

Figure 11-26 Classification of stability analysis approaches. 259

Figure 1127 Linguistic state space. 260

Figure 11-28 Linguistic trajectory. 261

Figure 13-1 Scope of data analysis. 280

Figure 13-2 Possible data structure in the plane. 282

Figure 13-3 Performance of cluster criteria. 283

Figure 13-4 Dendogram for hierarchical clusters. 283

Figure 13-5 Fuzzy graph. 285

Figure 13-6 Dendogram for graph-theoretic clusters. 285

Figure 13-7 The butterfly. 286

Figure 13-8 Crisp clusters of the butterfly. 287

Figure 13-9 Cluster 1 of the butterfly. 287

Figure 13-10 Cluster 2 of the butterfly. 288

Figure 13-11 Clusters for m＝1.25. 295

Figure 13-12 Clusters for m＝2. 295

Figure 13-13 Clusters by the FSC.（a） Data set; （b） circles found by FSC;（c）data set;（d）circles found by FSC. 300

Figure 13-14 Data sets [Krishnapuram and Keller 1993]. 301

Figure 13-15 Knowledge-based classification. 303

Figure 13-16 Linguistic variables “Depth of Cut” and “Feed”. 304

Figure 13-17 Knowledge base. 304

Figure 13-18 Basic structure of the knowledge-based system. 305

Figure 13-19 （a） States of objects at a point of time;（b） projections of trajectories over time into the feature space. 307

Figure 13-20 Structural and pointwise similarity. 308

Figure 13-21 Fictitious developments of share prices. 309

Figure 13-22 Idealized characteristic patterns of time signals for （a）an intact engine; （b） an engine with some defect. 309

Figure 13-23 （a） The fuzzy set “approximately zero” （μ（y））, the function f（t） and the resulting pointwise similarityμ（f（t））;（b）projection of pointwise similarity into the plane （t,μ（f（t）））. 311

Figure 13-24 Transformation of a feature vector containing trajectories into trajectories into a usual feature vector. 314

Figure 13-25 Input and output of the functional fuzzy c-means. 315

Figure 13-26 Structure of DataEngine. 318

Figure 13-27 Screen shot of DataEngine. 320

Figure 13-28 Cracking furnace. 324

Figure 13-29 Furnace temperature. 325

Figure 13-30 Fuzzy classification of continuous process. 325

Figure 13-31 Application of DataEngine for acoustic quality control. 327

Figure 14-1 A classical decision under certainty. 330

Figure 14-2 A fuzzy decision. 332

Figure 14-3 Optimal dividend as maximizing decision. 333

Figure 14-4 Feasible regions for μ？（x）＝0 and μ?（x）＝1 344

Figure 14-5 Fuzzy decision. 345

Figure 14-6 Basic structure of a dynamic programming model. 349

Figure 14-7 The vector-maximum problem. 355

Figure 14-8 Fuzzy LP with min-operator. 357

Figure 14-9 Fuzzy sets representing weights and ratings. 366

Figure 14-10 Final ratings of alternatives. 368

Figure 14-11 Preferability of alternative 2 over all others. 369

Figure 15-1 Linguistic values for variable “rigidity. 376

Figure 15-2 Linguistic values for variable “elements' rigidity”. 377

Figure 15-3 Linguistic values for variable “significance”. 379

Figure 15-4 Linguistic evaluation values of lathes B,C,D,E. 380

Figure 15-5 Membership functions resulting from incremental classifier design and classification of data obtained till point 440. 384

Figure 15-6 Membership functions for time window 〈230,330〉. 385

Figure 15-7 Membership functions for time window 〈240,340〉. 386

Figure 15-8 Membership functions for time window 〈250,350〉. 386

Figure 15-9 Proportional difference between class centers 1 and 2（with respect to the center of class 2） in time window〈250,350〉. 387

Figure 15-10 Membership functions for time window 〈3014,3114〉. 388

Figure 15-11 Membership functions for time window 〈3064,3200〉. 388

Figure 15-12 Road network. 392

Figure 15-13 Feasible covers. 392

Figure 15-14 i ne trapezoidai form of a fuzzy number ai＝（ai1,ai1,ai2,ai-2）. 394

Figure 15-15 The membership function of the fuzzy goal G. 394

Figure 15-16 The solution of the numerical example. 399

Figure 15-17 Structure of OPAL. 402

Figure 15-18 Fuzzy sets for the ratio in the “if”part of the rules. 404

Figure 15-19 Example of an FMS [Hartley 1984, p.194]. 405

Figure 15-20 Criteria hierarchies.（a） Release scheduling; （b）Machine scheduling. 407

Figure 15-21 Principle of approximate reasoning. 409

Figure 15-22 Membership functions for several linguistic terms. 413

Figure 15-23 Comparison of work force algorithms. 416

Figure 15-24 Flowtime of a course. 421

Figure 15-25 The scheduling process. 422

Figure 15-26 Courses of one instruction program. 424

Figure 15-27 Feature 1：current end-of-month balance for“Y”. 438

Figure 15-28 Feature 1: current end-of-month balance for“N”. 439

Figure 16-1 Calibration of the interval for measurement. 458

Figure 16-2 Subject 34, “Old Man”. 460

Figure 16-3 Subject 58, “Very Old Man”. 461

Figure 16-4 Subject 5, “Very Young Man”. 461

Figure 16-5 Subject 15, “Very Young Man”. 462

Figure 16-6 Subject 17, “Young Man”. 462

Figure 16-7 Subject 32, “Young Man”. 463

Figure 16-8 Empirical membership functions “Very Young Man”,“Young Man”,“Old Man”,“Very Old Man”. 464

Figure 16-9 Empirical unimodel membership functions“Very Young Man”,“Young Man”. 464

Figure 16-10 Min-operator: Observed vs.expected grades of membership. 468

Figure 16-11 Product-operator: Observed vs.expected grades of membership. 469

Figure 16-12 Predicted vs.observed data: Min-operator. 472

Figure 16-13 Predicted vs.observed data: Max-operator. 473

Figure 16-14 Predicted vs.observed data: Geometric mean operator. 473

Figure 16-15 Predicted vs.observed data: γ-operator. 474

Figure 16-16 Concept hierarchy of creditworthiness together with individual weights d and g-values for each level of aggregation. 475

Table 3-1 Classification of compensatory and noncompensatory operators. 39

Table 3-2 Classification of aggregation operators. 40

Table 3-3 Relationship between parameterized operators and their parameters. 41

Table 6-1 Properties of fuzzy relations. 89

Table 8-1 Rough taxonomy of uncertainty properties. 121

Table 8-2 Possibility functions. 128

Table 8-3 Koopman's vs.Kolmogoroff's probabilities. 136

Table 8-4 Relationship between Boolean algebra, probabilities,and possibilities. 137

Table 9-1 Formal quality of implication operators. 158

Table 10-1 Expert systems. 192

Table 10-2 A crisp data base. 196

Table 10-3 An extended data base. 196

Table 10-4 A possibilistic data base. 199

Table 10-5 α-level sets. 201

Table 11-1 Rule base. 230

Table 11-2 Properties of defuzzifiers. 238

Table 14-1 Ratings and weights of alternative goals. 367

Table 15-1 Selected applications in management and engineering. 374

Table 15-2 Experimental Data. 376

Table 15-3 Surface quality parameters （output data）. 376

Table 15-4 Boundary values of the linguistic variable“significance”. 378

Table 15-5a Populations. 391

Table 15-5b Distances between villages. 391

Table 15-6 Determination of the fuzzy set decision. 393

Table 15-7 Table of the parametric transportation problem. 397

Table 15-8 Solution to transportation problem. 398

Table 15-9 Membership grades for slack time and waiting time. 410

Table 15-10 Membership grades for conditional parts of the rules. 411

Table 15-11 Membership grades for the rules. 411

Table 15-12 Results. 412

Table 15-13 Definition of linguistic variables [Rinks 1982]. 414

Table 15-14 Membership functions. 415

Table 15-15 Cost results. 417

Table 15-16 Comparison of performances. 417

Table 15-17 Structure of instruction program. 423

Table 15-18 Availability of instructors. 425

Table 15-19 PERT output. 425

Table 15-20 Availability of weeks for courses. 426

Table 15-21 First week's final schedule. 426

Table 15-22 Cluster centers of nine optimal classes. 434

Table 15-23 Dynamic features describing bank customers. 434

Table 15-24 Main statistics of each feature of the data group“Y”. 435

Table 15-25 Main statistics of each feature of data group “N”. 435

Table 15-26 Scope of the analysis of bank customers. 436

Table 15-27 Absorbed and stray customers for “Y”-group. 437

Table 15-28 Absorbed and stray customers for “N”-group. 438

Table 15-29 Temporal change of assignment of customers in group“Y”to clusters. 439

Table 15-30 Temporal change of assignment of customers in group“N”to clusters. 439

Table 16-1 Hierarchy of scale levels. 451

Table 16-2 Empirically determined grades of membership. 455

Table 16-3 Empirical vs.predicted grades of membership. 467