Fuzzy measure theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Plenum Press
1992
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 354 S. graph. Darst. |
| ISBN: | 0306442604 |
Staff View
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| 245 | 1 | 0 | |a Fuzzy measure theory |c Zhenyuan Wang and George J. Klir |
| 264 | 1 | |a New York u.a. |b Plenum Press |c 1992 | |
| 300 | |a IX, 354 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Chapter 1. Introduction 1
Notes 5
Chapter 2. Required Background in Set Theory 7
2.1. Set Inclusion and Characteristic Function 7
2.2. Operations on Sets 9
2.3. Classes of Sets 15
2.4. Atoms and Holes 22
2.5. S Compact Spaces 28
2.6. Relations, Posets, and Lattices 30
Notes 34
Exercises 34
Chapter 3. Fuzzy Measures 39
3.1. Fuzzy Measures and Semicontinuous Fuzzy Measures .... 39
3.2. A Fuzzy Measures 42
3.3. Quasi measures 50
3.4. Belief Measures and Plausibility Measures 54
3.5. Possibility Measures and Necessity Measures 62
3.6. Properties of Finite Fuzzy Measures 66
Notes 68
Exercises 69
Chapter 4. Extensions 73
4.1. Extension of Quasi Measures and A Fuzzy Measures 73
4.2. Extension of Semicontinuous Fuzzy Measures 78
4.3. Absolute Continuity and Extension of Fuzzy Measures ... 81
4.4. Extension of Possibility Measures and Necessity Measures 84
Notes 91
Exercises 91
vii
viii Contents
Chapter 5. Structural Characteristics for Set Functions 95
5.1. Null Additivity 95
5.2. Autocontinuity 97
5.3. Uniform Autocontinuity 106
5.4. Structural Characteristics of Monotone Set Functions 107
5.5. Fuzzy Measures on S Compact Spaces 110
Notes Ill
Exercises Ill
Chapter 6. Measurable Functions on Fuzzy Measure Spaces 115
6.1. Measurable Functions 115
6.2. Almost and Pseudo Almost 117
6.3. Relation Among Convergences of Measurable Function
Sequence 120
6.4. Convergences of Measurable Function Sequence on
Possibility Measure Spaces 126
Notes 128
Exercises 128
Chapter 7. Fuzzy Integrals 131
7.1. Definition 131
7.2. Properties of the Fuzzy Integral 135
7.3. Convergence Theorems of the Fuzzy Integral Sequence ... 143
7.4. Transformation Theorem for Fuzzy Integrals 152
7.5. Fuzzy Measures Defined by Fuzzy Integrals 154
7.6. Fuzzy Integrals with Respect to a Nonnegative Monotone
Set Function 157
Notes 159
Exercises 160
Chapter 8. Pan Integrals 163
8.1. Pan Additions and Pan Multiplications 163
8.2. Definition of Pan Integral 164
8.3. Properties of Pan Integral 168
8.4. A Transformation Theorem 170
Notes 173
Exercises 173
Contents ix
Chapter 9. Applications 175
9.1. General Remarks 175
9.2. Dempster Shafer Theory 176
9.3. Possibility Theory 181
9.4. Fuzzy Measures and Fuzzy Integrals 184
9.5. Fuzzy Convolution of Fuzzy Distributions 190
Notes 192
References 195
Appendix A. Some Concepts and Results Regarding Classical Measures 203
Appendix B. Some Concepts and Results Regarding Fuzzy Sets 209
Appendix C. Glossary of Key Concepts 219
Appendix D. Glossary of Symbols 227
Appendix E. New Directions in Fuzzy Measure Theory 231
Appendix F. Representative Applications of Fuzzy Measure Theory 285
Author Index 343
Subject Index 347
|
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| id | DE-604.BV006981659 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:53:12Z |
| institution | BVB |
| isbn | 0306442604 |
| language | English |
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| physical | IX, 354 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Plenum Press |
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| spelling | Wang, Zhenyuan Verfasser (DE-588)13782503X aut Fuzzy measure theory Zhenyuan Wang and George J. Klir New York u.a. Plenum Press 1992 IX, 354 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fuzzy sets gtt Fuzzy measure theory Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Messtheorie (DE-588)4169537-9 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Messtheorie (DE-588)4169537-9 s Fuzzy-Menge (DE-588)4061868-7 s DE-604 Maßtheorie (DE-588)4074626-4 s DE-188 Klir, George J. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004416621&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wang, Zhenyuan Klir, George J. Fuzzy measure theory Fuzzy sets gtt Fuzzy measure theory Fuzzy-Menge (DE-588)4061868-7 gnd Messtheorie (DE-588)4169537-9 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4061868-7 (DE-588)4169537-9 (DE-588)4074626-4 |
| title | Fuzzy measure theory |
| title_auth | Fuzzy measure theory |
| title_exact_search | Fuzzy measure theory |
| title_full | Fuzzy measure theory Zhenyuan Wang and George J. Klir |
| title_fullStr | Fuzzy measure theory Zhenyuan Wang and George J. Klir |
| title_full_unstemmed | Fuzzy measure theory Zhenyuan Wang and George J. Klir |
| title_short | Fuzzy measure theory |
| title_sort | fuzzy measure theory |
| topic | Fuzzy sets gtt Fuzzy measure theory Fuzzy-Menge (DE-588)4061868-7 gnd Messtheorie (DE-588)4169537-9 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Fuzzy sets Fuzzy measure theory Fuzzy-Menge Messtheorie Maßtheorie |
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