Uncertainty theory: a branch of mathematics for modeling human uncertainty
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Schriftenreihe: | Studies in computational intelligence
300 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XI, 350 S. graph. Darst. |
| ISBN: | 9783642139581 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text |
IMAGE 1
C O N T E N T S
PREFACE I X
1 U N C E R T A I N T Y T H E O R Y 1
1.1 UNCERTAIN MEASURE 1
1.2 UNCERTAIN VARIABLE 11
1.3 UNCERTAINTY DISTRIBUTION 14
1.4 INDEPENDENCE 21
1.5 OPERATIONAL LAW 23
1.6 E X P E C T E D VALUE 44
1.7 VARIANCE 52
1.8 MOMENTS 54
1.9 CRITICAL VALUES 56
1.10 E N T R O P Y 60
1.11 DISTANCE 66
1.12 INEQUALITIES 67
1.13 CONVERGENCE CONCEPTS 69
1.14 CONDITIONAL UNCERTAINTY 74
2 U N C E R T A I N P R O G R A M M I N G 8 1
2.1 R A N K I N G CRITERIA 8 1
2.2 E X P E C T E D VALUE MODEL 82
2.3 CHANCE-CONSTRAINED P R O G R A M M I N G 83
2.4 DEPENDENT-CHANCE P R O G R A M M I N G 88
2.5 UNCERTAIN DYNAMIC P R O G R A M M I N G 9 3
2.6 UNCERTAIN MULTILEVEL P R O G R A M M I N G 94
2.7 HYBRID INTELLIGENT ALGORITHM 98
2.8 $ G R A P H 99
2.9 P R O J E C T SCHEDULING P R O B L E M 100
2.10 ' VEHICLE R O U T I N G P R O B L E M 103
2.11 MACHINE SCHEDULING P R O B L E M 108
2.12 EXERCISES 112
3 U N C E R T A I N R I S K A N A L Y S I S 1 1 5
3.1 RISK INDEX 115
3.2 H A Z A R D DISTRIBUTION 118
3.3 BOOLEAN SYSTEM 120
3.4 RISK INDEX CALCULATOR 122
HTTP://D-NB.INFO/1002680573
IMAGE 2
VI C O N T E N T S
4 U N C E R T A I N R E L I A B I L I T Y A N A L Y S I S 1 2 5
4.1 RELIABILITY INDEX 125
4.2 CONDITIONAL RELIABILITY 127
4.3 BOOLEAN SYSTEM 128
4.4 RELIABILITY INDEX CALCULATOR 130
5 U N C E R T A I N P R O C E S S 1 3 1
5.1 UNCERTAIN PROCESS 131
5.2 R.ENEWAL PROCESS 132
5.3 MARTINGALE 138
5.4 MARKOV PROCESS 138
5.5 STATIONARY PROCESS 138
6 U N C E R T A I N C A L C U L U S 1 3 9
6.1 CANONICAL PROCESS 139
6.2 UNCERTAIN INTEGRAL 141
6.3 C H A I N RULE 143
6.4 INTEGRATION BY P A R T S 144
7 U N C E R T A I N D I F F E R E N T I A L E Q U A T I O N 1 4 7
7.1 UNCERTAIN DIFFERENTIAL E Q U A T I O N 147
7.2 EXISTENCE A N D UNIQUENESS T H E O R E M 149
7.3 STABILITY T H E O R E M 151
7.4 NUMERICAL M E T H O D 152
7.5 UNCERTAIN DIFFERENTIAL E Q U A T I O N W I T H J U M P S 156
7.6 UNCERTAIN FINANCE 158
8 U N C E R T A I N L O G I C 1 6 3
8.1 UNCERTAIN PROPOSITION 163
8.2 CONNECTIVE SYMBOLS 164
8.3 UNCERTAIN FORMULA 164
8.4 T R U T H FUNCTION 164
8.5 T R U T H VALUE 165
8.6 T R U T H VALUE T H E O R E M 166
8.7 TRUTH, VALUE SOLVER 173
8.8 UNCERTAIN P R E D I C A T E LOGIC 174
9 U N C E R T A I N E N T A I L M E N T 1 7 7
9.1 ENTAILMENT MODEL 177
9.2 M O D U S PONENS 182
9.3 MODUS TOLLENS 184
9.4 HYPOTHETICAL SYLLOGISM 185
9.5 A U T O M A T I C E N T A I L M E N T MACHINE 186
IMAGE 3
C O N T E N T S V I I
1 0 U N C E R T A I N S E T T H E O R Y 1 8 7
10.1 UNCERTAIN SET 187
10.2 MEMBERSHIP DEGREE 190
10.3 MEMBERSHIP FUNCTION 192
10.4 UNCERTAINTY DISTRIBUTION 199
10.5 INDEPENDENCE 201
10.6 OPERATIONAL LAW 203
10.7 E X P E C T E D VALUE 206
10.8 CRITICAL VALUES 210
10.9 HAUSDORFF DISTANCE 212
10.10 CONDITIONAL UNCERTAINTY 213
11 U N C E R T A I N I N F E R E N C E 2 1 5
11.1 INFERENCE RULE 215
11.2 UNCERTAIN SYSTEM 219
11.3 INFERENCE CONTROL 222
11.4 INVERTED P E N D U L U M 223
A S U P P L E M E N T S 2 2 5
A. 1 LAW OF T R U T H CONSERVATION 225
A.2 M A X I M U M UNCERTAINTY PRINCIPLE 225
A.3 HOW T O DETERMINE DISTRIBUTION? 226
A.4 EVOLUTION OF MEASURES 229
A.5 UNCERTAINTY VS. RANDOMNESS 232
A.6 UNCERTAINTY + R A N D O M N E S S 233
A.7 UNCERTAINTY VS. FUZZINESS 236
A.8 W H A T IS UNCERTAINTY? 237
B P R O B A B I L I T Y T H E O R Y 2 3 9
B . L PROBABILITY SPACE 239
B.2 R A N D O M VARIABLE 242
B.3 PROBABILITY DISTRIBUTION 244
B.4 INDEPENDENCE 247
B.5 E X P E C T E D VALUE 248
B.6 VARIANCE 254
B.7 MOMENTS 255
B.8 CRITICAL VALUES 256
B.9 E N T R O P Y . . 257
B.10 CONDITIONAL PROBABILITY 261
B . L L R A N D O M SET 263
C C R E D I B I L I T Y T H E O R Y 2 6 7
C . L CREDIBILITY SPACE 267
C.2 FUZZY VARIABLE 277
C.3 MEMBERSHIP FUNCTION 288
C.4 CREDIBILITY DISTRIBUTION 282
IMAGE 4
VIII C O N T E N T S
C.5 INDEPENDENCE 284
C.6 EXTENSION PRINCIPLE OF Z A D E H 286
C.7 E X P E C T E D VALUE 288
C.8 VARIANCE 293
C.9 MOMENTS 295
C.10 CRITICAL VALUES 295
C . L L E N T R O P Y 297
C.12 CONDITIONAL CREDIBILITY 302
C.13 FUZZY SET 306
D C H A N C E T H E O R Y 3 0 9
D . L CHANCE SPACE 309
D.2 HYBRID VARIABLE 317
D.3 CHANCE DISTRIBUTION 323
D.4 E X P E C T E D VALUE 324
D.5 VARIANCE 326
D.6 CRITICAL VALUES 326
D.7 CONDITIONAL CHANCE 328
B I B L I O G R A P H Y 3 3 3
L I S T O F F R E Q U E N T L Y U S E D S Y M B O L S 3 4 6
F I V E P L U S O N E 3 4 7
I N D E X 3 4 9 |
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| institution | BVB |
| isbn | 9783642139581 |
| language | English |
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| physical | XI, 350 S. graph. Darst. |
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| series | Studies in computational intelligence |
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| spelling | Liu, Baoding 1965- Verfasser (DE-588)12374539X aut Uncertainty theory a branch of mathematics for modeling human uncertainty Baoding Liu Berlin [u.a.] Springer 2010 XI, 350 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in computational intelligence 300 Ungewissheit (DE-588)4137198-7 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Ungewissheit (DE-588)4137198-7 s Mathematik (DE-588)4037944-9 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-13959-8 Studies in computational intelligence 300 (DE-604)BV020822171 300 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3480863&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025193972&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liu, Baoding 1965- Uncertainty theory a branch of mathematics for modeling human uncertainty Studies in computational intelligence Ungewissheit (DE-588)4137198-7 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4137198-7 (DE-588)4037944-9 |
| title | Uncertainty theory a branch of mathematics for modeling human uncertainty |
| title_auth | Uncertainty theory a branch of mathematics for modeling human uncertainty |
| title_exact_search | Uncertainty theory a branch of mathematics for modeling human uncertainty |
| title_full | Uncertainty theory a branch of mathematics for modeling human uncertainty Baoding Liu |
| title_fullStr | Uncertainty theory a branch of mathematics for modeling human uncertainty Baoding Liu |
| title_full_unstemmed | Uncertainty theory a branch of mathematics for modeling human uncertainty Baoding Liu |
| title_short | Uncertainty theory |
| title_sort | uncertainty theory a branch of mathematics for modeling human uncertainty |
| title_sub | a branch of mathematics for modeling human uncertainty |
| topic | Ungewissheit (DE-588)4137198-7 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Ungewissheit Mathematik |
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