Fuzzy set theory - and its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Kluwer Acad. Publ.
2001
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| Edition: | 4. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXV, 514 S. Ill., graph. Darst. |
| ISBN: | 0792374355 |
Staff View
MARC
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| 100 | 1 | |a Zimmermann, Hans-Jürgen |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fuzzy set theory - and its applications |c H.-J. Zimmermann |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Kluwer Acad. Publ. |c 2001 | |
| 300 | |a XXV, 514 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804129241375178752 |
|---|---|
| adam_text | Contents
List of Figures ix
List of Tables xiii
Foreword xv
Preface xvii
Preface to the Fourth Edition xix
1 Introduction to Fuzzy Sets 1
1.1 Crispness, Vagueness, Fuzziness, Uncertainty 1
1.2 Fuzzy Set Theory 2
Part I: 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
vi CONTENTS
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 II: 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
CONTENTS Vii
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
viii CONTENTS
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
|
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| indexdate | 2024-07-09T19:02:00Z |
| institution | BVB |
| isbn | 0792374355 |
| language | English |
| lccn | 2001038123 |
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| physical | XXV, 514 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| spelling | Zimmermann, Hans-Jürgen Verfasser aut Fuzzy set theory - and its applications H.-J. Zimmermann 4. ed. Boston [u.a.] Kluwer Acad. Publ. 2001 XXV, 514 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fuzzy sets Operations research Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf Operations Research (DE-588)4043586-6 s Fuzzy-Menge (DE-588)4061868-7 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009838961&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zimmermann, Hans-Jürgen Fuzzy set theory - and its applications Fuzzy sets Operations research Fuzzy-Menge (DE-588)4061868-7 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4061868-7 (DE-588)4043586-6 |
| title | Fuzzy set theory - and its applications |
| title_auth | Fuzzy set theory - and its applications |
| title_exact_search | Fuzzy set theory - and its applications |
| title_full | Fuzzy set theory - and its applications H.-J. Zimmermann |
| title_fullStr | Fuzzy set theory - and its applications H.-J. Zimmermann |
| title_full_unstemmed | Fuzzy set theory - and its applications H.-J. Zimmermann |
| title_short | Fuzzy set theory - and its applications |
| title_sort | fuzzy set theory and its applications |
| topic | Fuzzy sets Operations research Fuzzy-Menge (DE-588)4061868-7 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Fuzzy sets Operations research Fuzzy-Menge Operations Research |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009838961&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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