模糊集合论及其应用 第4版 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

模糊集合论及其应用 第4版 英文PDF格式电子书版下载

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1 Introduction to Fuzzy Sets1

1.1 Crispness, Vagueness, Fuzziness, Uncertainty1

1.2 Fuzzy Set Theory2

PartⅠ: Fuzzy Mathematics9

2 Fuzzy Sets-Basic Definitions11

2.1 Basic Definitions11

2.2 Basic Set-Theoretic Operations for Fuzzy Sets16

3 Extensions23

3.1 Types of Fuzzy Sets23

3.2 Further Operations on Fuzzy Sets27

3.2.1 Algebraic Operations28

3.2.2 Set-Theoretic Operations29

3.2.3 Criteria for Selecting Appropriate Aggregation Operators43

4 Fuzzy Measures and Measures of Fuzziness47

4.1 Fuzzy Measures47

4.2 Measures of Fuzziness49

5 The Extension Principle and Applications55

5.1 The Extension Principle55

5.2 Operations for Type 2 Fuzzy Sets56

5.3 Algebraic Operations with Fuzzy Numbers59

5.3.1 Special Extended Operations61

5.3.2 Extended Operations for LR-Representation of Fuzzy Sets64

6 Fuzzy Relations and Fuzzy Graphs71

6.1 Fuzzy Relations on Sets and Fuzzy Sets71

6.1.1 Compositions of Fuzzy Relations76

6.1.2 Properties of the Min-Max Composition79

6.2 Fuzzy Graphs83

6.3 Special Fuzzy Relations86

7 Fuzzy Analysis93

7.1 Fuzzy Functions on Fuzzy Sets93

7.2 Extrema of Fuzzy Functions95

7.3 Integration of Fuzzy Functions99

7.3.1 Integration of a Fuzzy Function over a Crisp Interval100

7.3.2 Integration of a （Crisp） Real-Valued Function over a Fuzzy Interval103

7.4 Fuzzy Differentiation107

8 Uncertainty Modeling111

8.1 Application-oriented Modeling of Uncertainty111

8.1.1 Causes of Uncertainty114

8.1.2 Type of Available Information117

8.1.3 Uncertainty Methods118

8.1.4 Uncertainty Theories as Transformers of Information119

8.1.5 Matching Uncertainty Theory and Uncertain Phenomena120

8.2 Possibility Theory122

8.2.1 Fuzzy Sets and Possibility Distributions122

8.2.2 Possibility and Necessity Measures126

8.3 Probability of Fuzzy Events129

8.3.1 Probability of a Fuzzy Event as a Scalar129

8.3.2 Probability of a Fuzzy Event as a Fuzzy Set131

8.4 Possibility vs.Probability133

Part I: Applications of Fuzzy Set Theory139

9 Fuzzy Logic and Approximate Reasoning141

9.1 Linguistic Variables141

9.2 Fuzzy Logic149

9.2.1 Classical Logics Revisited149

9.2.2 Linguistic Truth Tables153

9.3 Approximate and Plausible Reasoning156

9.4 Fuzzy Languages160

9.5 Support Logic Programming and Fril169

9.5.1 Introduction169

9.5.2 Fril Rules170

9.5.3 Inference Methods in Fril172

9.5.4 Fril Inference for a Single Rule175

9.5.5 Multiple Rule Case176

9.5.6 Interval and Point Semantic Unification177

9.5.7 Least Prejudiced Distribution and Learning179

9.5.8 Applications of Fril181

10 Fuzzy Sets and Expert Systems185

10.1 Introduction to Expert Systems185

10.2 Uncertainty Modeling in Expert Systems193

10.3 Applications203

11 Fuzzy Control223

11.1 Origin and Objective223

11.2 Automatic Control225

11.3 The Fuzzy Controller226

11.4 Types of Fuzzy Controllers228

11.4.1 The Mamdani Controller228

11.4.2 Defuzzification232

11.4.3 The Sugeno Controller239

11.5 Design Parameters240

11.5.1 Scaling Factors240

11.5.2 Fuzzy Sets240

11.5.3 Rules242

11.6 Adaptive Fuzzy Control243

11.7 Applications244

11.7.1 Crane Control244

11.7.2 Control of a Model Car246

11.7.3 Control of a Diesel Engine248

11.7.4 Fuzzy Control of a Cement Kiln249

11.8 Tools255

11.9 Stability257

11.10 Extensions262

12 Fuzzy Data Bases and Queries265

12.1 Introduction265

12.2 Fuzzy Relational Databases266

12.3 Fuzzy Queries in Crisp Databases268

13 Fuzzy Data Analysis277

13.1 Introduction277

13.2 Methods for Fuzzy Data Analysis279

13.2.1 Algorithmic Approaches281

13.2.2 Knowledge-Based Approaches302

13.2.3 Neural Net Approaches304

13.3 Dynamic Fuzzy Data Analysis306

13.3.1 Problem Description306

13.3.2 Similarity of Functions307

13.3.3 Approaches for Analysic Dynamic Systems313

13.4 Tools for Fuzzy Data Analysis317

13.4.1 Requirements for FDA Tools317

13.4.2 Data Engine318

13.5 Applications of FDA322

13.5.1 Maintenance Management in Petrochemical Plants322

13.5.2 Acoustic Quality Control323

14 Decision Making in Fuzzy Environments329

14.1 Fuzzy Decisions329

14.2 Fuzzy Linear Programming336

14.2.1 Symmetric Fuzzy LP337

14.2.2 Fuzzy LP with Crisp Objective Function342

14.3 Fuzzy Dynamic Programming348

14.3.1 Fuzzy Dynamic Programming with Crisp State Transformation Function349

14.4 Fuzzy Multicriteria Analysis352

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 Management371

15.1 Introduction371

15.2 Engineering Applications373

15.2.1 Linguistic Evaluation and Ranking of Machine Tools375

15.2.2 Fault Detection in Gearboxes381

15.3 Applications in Management389

15.3.1 A Discrete Location Model390

15.3.2 Fuzzy Set Models in Logistics393

15.3.2.1 Fuzzy Approach to the Transportation Problem393

15.3.2.2 Fuzzy Linear Programming in Logistics398

15.3.3 Fuzzy Sets in Scheduling401

15.3.3.1 Job-Shop Scheduling with Expert Systems401

15.3.3.2 A Method to Control Flexible Manufacturing Systems405

15.3.3.3 Aggregate Production and Inventory Planning411

15.3.3.4 Fuzzy Mathematical Programming for Maintenance Scheduling418

15.3.3.5 Scheduling Courses, Instructors, and Classrooms419

15.3.4 Fuzzy Set Models in Inventory Control426

15.3.5 Fuzzy Sets in Marketing432

15.3.5.1 Customer Segmentation in Banking and Finance432

15.3.5.2 Bank Customer Segmentation based on Customer Behavior433

16 Empirical Research in Fuzzy Set Theory443

16.1 Formal Theories vs& Factual Theories vs.Decision Technologies443

16.1.1 Models in Operations Research and Management Science447

16.1.2 Testing Factual Models449

16.2 Empirical Research on Membership Functions453

16.2.1 Type A-Membership Model454

16.2.2 Type B-Membership Model456

16.3 Empirical Research on Aggregators463

16.4 Conclusions474

17 Future Perspectives477

Abbreviations of Frequently Cited Journals481

Bibliography483

Index507

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）＝1344

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