Fuzzy set theory and its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Kluwer Acad. Publ.
1991
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| Edition: | 2., rev. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 399 S. |
| ISBN: | 079239075X |
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 2., rev. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Kluwer Acad. Publ. |c 1991 | |
| 300 | |a XIV, 399 S. | ||
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Record in the Search Index
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| adam_text | Contents
List of Figures ix
List of Tables xiii
Foreword xv
Preface xvii
Preface for the Revised Edition xix
1 Introduction to Fuzzy Sets 1
1-1 Crispness, Vagueness, Fuzziness, Uncertainty 1
1.2 Fuzzy Set Theory 5
Part One: Fuzzy Mathematics g
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 28
3.2.1 Algebraic Operations 28
3.2.2 Set-Theoretic Operations 29
3.2.3 Criteria for Selecting Appropriate Aggregation Operators 39
4 Fuzzy Measures and Measures of Fuzziness 45
4.1 Fuzzy Measures 45
4.2 Measures of Fuzziness 47
5 The Extension Principle and Applications 53
5.1 The Extension Principle 53
5.2 Operations for Type 2 Fuzzy Sets 55
5.3 Algebraic Operations with Fuzzy Numbers 57
v
vi CONTENTS
5.3.1 Special Extended Operations 59
5.3.2 Extended Operations for /.^-Representation of Fuzzy Sets 62
6 Fuzzy Relations and Fuzzy Graphs 69
6.1 Fuzzy Relations on Sets and Fuzzy Sets 69
6.1.1 Compositions of Fuzzy Relations 74
6.1.2 Properties of the Min-Max Composition 77
6.2 Fuzzy Graphs 82
6.3 Special Fuzzy Relations 85
7 Fuzzy Analysis 91
7.1 Fuzzy Functions on Fuzzy Sets 91
7.2 Extrema of Fuzzy Functions 93
7.3 Integration of Fuzzy Functions 98
7.3.1 Integration of a Fuzzy Function over a Crisp Interval 98
7.3.2 Integration of a (Crisp) Real-Valued Function over a Fuzzy 101
Interval
7.4 Fuzzy Differentiation 105
8 Possibility Theory, Probability Theory, and Fuzzy Set 109
Theory
8.1 Possibility Theory 110
8.1.1 Fuzzy Sets and Possibility Distributions 110
8.1.2 Possibility and Necessity Measures 114
8.2 Probability of Fuzzy Events 117
8.2.1 Probability of a Fuzzy Event as a Scalar 118
8.2.2 Probability of a Fuzzy Event as a Fuzzy Set 119
8.3 Possibility vs. Probability 121
Part Two: Applications of Fuzzy Set Theory 129
9 Fuzzy Logic and Approximate Reasoning 131
9.1 Linguistic Variables 131
9.2 Fuzzy Logic 139
9.2.1 Classical Logics Revisited 139
9.2.2 Truth Tables and Linguistic Approximation 143
9.3 Approximate Reasoning 146
9.4 Fuzzy Languages 148
9.5 Support Logic Programming 157
9.5.1 Support Horn Clause Logic Representation 158
9.5.2 Approximate Reasoning in SLOP 162
10 Expert Systems and Fuzzy Control 171
10.1 Fuzzy Sets and Expert Systems 171
10.1.1 Introduction to Expert Systems 171
10.1.2 Uncertainty Modeling in Expert Systems 179
10.1.3 Applications 182
10.2 Fuzzy Control 201
CONTENTS vii
10.2.1 Introduction to Fuzzy Control 201
10.2.2 Process of Fuzzy Control 202
10.2.3 Applications of Fuzzy Control 209
11 Pattern Recognition 217
11.1 Models for Pattern Recognition 217
11.1.1 The Data 219
11.1.2 Structure or Pattern Space 219
11.1.3 Feature Space and Feature Selection 219
11.1.4 Classification and Classification Space 220
11.2 Fuzzy Clustering 220
11.2.1 Clustering Methods 220
11.2.2 Cluster Validity 236
12 Decision Making in Fuzzy Environments 241
12.1 Fuzzy Decisions 241
12.2 Fuzzy Linear Programming 248
12.2.1 Symmetric Fuzzy LP 250
12.2.2 Fuzzy LP with Crisp Objective Function 254
12.3 Fuzzy Dynamic Programming 261
12.4 Fuzzy Multi Criteria Analysis 265
12.4.1 Multi Objective Decision Making 265
12.4.2 Multi Attributive Decision Making 272
13 Fuzzy Set Models in Operations Research 283
13.1 Introduction 283
13.2 Fuzzy Set Models in Logistics 285
13.2.1 Fuzzy Approach to the Transportation Problem 286
13.2.2 Fuzzy Linear Programming in Logistics 290
13.3 Fuzzy Set Models in Production Control and Scheduling 293
13.3.1 A Fuzzy Set Decision Model as Optimization Criterion 294
13.3.2 Job-Shop Scheduling with Expert Systems 296
13.3.3 A Method to Control Flexible Manufacturing Systems 299
13.3.4 Aggregate Production and Inventory Planning 307
13.3.5 Fuzzy Mathematical Programming for Maintenance 313
Scheduling
13.3.6 Scheduling Courses, Instructors, and Classrooms 314
13.4 Fuzzy Set Models in Inventory Control 321
13.5 A Discrete Location Model 327
14 Empirical Research in Fuzzy Set Theory 333
14.1 Formal Theories vs. Factual Theories vs. Decision 333
Technologies
14.1.1 Models in Operations Research and Management Science 337
14.1.2 Testing Factual Models 339
14.2 Empirical Research on Membership Functions 344
14.2.1 Type A-Membership Model 345
14.2.2 Type B-Membership Model 346
viii CONTENTS
14.3 Empirical Research on Aggregators 355
14.4 Conclusions 367
15 Future Perspectives 369
Bibliography 373
Index 393
|
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| author_facet | Zimmermann, Hans-Jürgen |
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| discipline | Psychologie Mathematik Wirtschaftswissenschaften |
| edition | 2., rev. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:15:11Z |
| institution | BVB |
| isbn | 079239075X |
| language | English |
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| physical | XIV, 399 S. |
| publishDate | 1991 |
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| publisher | Kluwer Acad. Publ. |
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| spelling | Zimmermann, Hans-Jürgen Verfasser aut Fuzzy set theory and its applications H.-J. Zimmermann 2., rev. ed. Boston [u.a.] Kluwer Acad. Publ. 1991 XIV, 399 S. txt rdacontent n rdamedia nc rdacarrier Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf Fuzzy-Menge (DE-588)4061868-7 s DE-604 Operations Research (DE-588)4043586-6 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019176646&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zimmermann, Hans-Jürgen Fuzzy set theory and its applications 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-Menge (DE-588)4061868-7 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Fuzzy-Menge Operations Research |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019176646&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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