Uncertainty theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Dordrecht ; London
Springer
[2015]
|
| Edition: | Fourth edition |
| Series: | Springer uncertainty research
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Frühere Auflagen erschienen in der Springer Serie: "Studies in fuzziness and soft computing" Literaturverzeichnis: Seite 467-482 |
| Physical Description: | xv, 485 Seiten Diagramme |
| ISBN: | 9783662443538 3662443538 9783662443545 |
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CONTENTS
PREFACE XI
0 INTRODUCTION 1
0.1 INDETERMINACY 1
0.2 FREQUENCY 2
0.3 BELIEF DEGREE 3
0.4 SUMMARY 7
1 UNCERTAIN MEASURE 9
1.1 MEASURABLE SPACE 9
1.2 EVENT 11
1.3 UNCERTAIN MEASURE 12
1.4 UNCERTAINTY SPACE 16
1.5 PRODUCT UNCERTAIN MEASURE 16
1.6 INDEPENDENCE 21
1.7 POLYRCCTANGULAR THEOREM 23
1.8 CONDITIONAL UNCERTAIN MEASURE 25
1.9 BIBLIOGRAPHIC NOTES 28
2 UNCERTAIN VARIABLE 29
2.1 UNCERTAIN VARIABLE 29
2.2 UNCERTAINTY DISTRIBUTION 31
2.3 INDEPENDENCE 43
2.4 OPERATIONAL LAW 44
2.5 EXPECTED VALUE 66
2.6 VARIANCE 76
2.7 MOMENT 79
2.8 ENTROPY 82
2.9 DISTANCE 88
2.10 CONDITIONAL UNCERTAINTY DISTRIBUTION 90
2.11 UNCERTAIN SEQUENCE 93
2.12 UNCERTAIN VECTOR 98
2.13 BIBLIOGRAPHIC NOTES 102
HTTP://D-NB.INFO/1053174942
VI
CONTENTS
3 UNCERTAIN PROGRAMMING 105
3.1 UNCERTAIN PROGRAMMING 105
3.2 NUMERICAL METHOD 108
3.3 MACHINE SCHEDULING PROBLEM 110
3.4 VEHICLE ROUTING PROBLEM 113
3.5 PROJECT SCHEDULING PROBLEM 117
3.6 UNCERTAIN MULTIOBJECTIVE PROGRAMMING 121
3.7 UNCERTAIN GOAL PROGRAMMING 122
3.8 UNCERTAIN MULTILEVEL PROGRAMMING 123
3.9 BIBLIOGRAPHIC NOTES 124
4 UNCERTAIN STATISTICS 127
4.1 EXPERT'S EXPERIMENTAL DATA 127
4.2 QUESTIONNAIRE SURVEY 128
4.3 EMPIRICAL UNCERTAINTY DISTRIBUTION 129
4.4 PRINCIPLE OF LEAST SQUARES 130
4.5 METHOD OF MOMENTS 132
4.6 MULTIPLE DOMAIN EXPERTS 133
4.7 DELPHI METHOD 134
4.8 BIBLIOGRAPHIC NOTES 135
5 UNCERTAIN RISK ANALYSIS 137
5.1 LOSS FUNCTION 137
5.2 RISK INDEX 139
5.3 SERIES SYSTEM 140
5.4 PARALLEL SYSTEM 140
5.5 FC-OUT-OF-N SYSTEM 141
5.6 STANDBY SYSTEM 141
5.7 STRUCTURAL RISK ANALYSIS 142
5.8 INVESTMENT RISK ANALYSIS 145
5.9 VALUE-AT-RISK 146
5.10 EXPECTED LOSS 147
5.11 HAZARD DISTRIBUTION 148
5.12 BIBLIOGRAPHIC NOTES 149
6 UNCERTAIN RELIABILITY ANALYSIS 151
6.1 STRUCTURE FUNCTION 151
6.2 RELIABILITY INDEX 152
6.3 SERIES SYSTEM 153
6.4 PARALLEL SYSTEM 153
6.5 FC-OUT-OF-N SYSTEM 154
6.6 GENERAL SYSTEM 154
6.7 BIBLIOGRAPHIC NOTES 155
CONTENTS
VII
7 UNCERTAIN PROPOSITIONAL LOGIC 157
7.1 UNCERTAIN PROPOSITION 157
7.2 TVUTH VALUE 159
7.3 CHEN-RALESCU THEOREM 161
7.4 BOOLEAN SYSTEM CALCULATOR 163
7.5 UNCERTAIN PREDICATE LOGIC 163
7.6 BIBLIOGRAPHIC NOTES 167
8 UNCERTAIN ENTAILMENT 169
8.1 UNCERTAIN ENTAILMENT, MODEL 169
8.2 UNCERTAIN MODUS PONENS 171
8.3 UNCERTAIN MODUS TOLLENS 172
8.4 UNCERTAIN HYPOTHETICAL SYLLOGISM 174
8.5 BIBLIOGRAPHIC NOTES 175
9 UNCERTAIN SET 177
9.1 UNCERTAIN SET 177
9.2 MEMBERSHIP FUNCTION 183
9.3 INDEPENDENCE 192
9.4 SET OPERATIONAL LAW 196
9.5 ARITHMETIC OPERATIONAL LAW 200
9.6 EXPECTED VALUE 204
9.7 VARIANCE 210
9.8 ENTROPY 211
9.9 DISTANCE 215
9.10 CONDITIONAL MEMBERSHIP FUNCTION 216
9.11 UNCERTAIN STATISTICS 216
9.12 BIBLIOGRAPHIC NOTES 220
10 UNCERTAIN LOGIC 221
10.1 INDIVIDUAL FEATURE DATA 221
10.2 UNCERTAIN QUANTIFIER 222
10.3 UNCERTAIN SUBJECT 229
10.4 UNCERTAIN PREDICATE 232
10.5 UNCERTAIN PROPOSITION 235
10.6 TRUTH VALUE 236
10.7 ALGORITHM 240
10.8 LINGUISTIC SUNNNARIZER 243
10.9 BIBLIOGRAPHIC NOTES 246
11 UNCERTAIN INFERENCE 247
11.1 UNCERTAIN INFERENCE RULE 247
11.2 UNCERTAIN SYSTEM 251
11.3 UNCERTAIN CONTROL 255
11.4 INVERTED PENDULUM 255
VIII
CONTENTS
11.5 BIBLIOGRAPHIC NOTES 257
12 UNCERTAIN PROCESS 259
12.1 UNCERTAIN PROCESS 259
12.2 UNCERTAINTY DISTRIBUTION 261
12.3 INDEPENDENCE AND OPERATIONAL LAW 265
12.4 INDEPENDENT INCREMENT PROCESS 266
12.5 STATIONARY INDEPENDENT INCREMENT PROCESS 268
12.6 EXTREME VALUE THEOREM 273
12.7 FIRST HITTING TIME 277
12.8 TIME INTEGRAL 280
12.9 BIBLIOGRAPHIC NOTES 282
13 UNCERTAIN RENEWAL PROCESS 283
13.1 UNCERTAIN RENEWAL PROCESS 283
13.2 BLOCK REPLACEMENT POLICY 287
13.3 RENEWAL REWARD PROCESS 288
13.4 UNCERTAIN INSURANCE MODEL 290
13.5 AGE REPLACEMENT, POLICY 294
13.6 ALTERNATING RENEWAL PROCESS 298
13.7 BIBLIOGRAPHIC NOTES 302
14 UNCERTAIN CALCULUS 303
14.1 LIU PROCESS 303
14.2 LIU INTEGRAL 308
14.3 FUNDAMENTAL THEOREM 313
14.4 CHAIN RULE 315
14.5 CHANGE OF VARIABLES 315
14.6 INTEGRATION BY PARTS 316
14.7 BIBLIOGRAPHIC NOTES 318
15 UNCERTAIN DIFFERENTIAL EQUATION 319
15.1 UNCERTAIN DIFFERENTIAL EQUATION 319
15.2 ANALYTIC METHODS 322
15.3 EXISTENCE AND UNIQUENESS 327
15.4 STABILITY 329
15.5 A-PATH 331
15.6 YAO-CHEN FORMULA 332
15.7 NUMERICAL METHODS 343
15.8 BIBLIOGRAPHIC NOTES 345
16 UNCERTAIN FINANCE 347
16.1 UNCERTAIN STOCK MODEL 347
16.2 UNCERTAIN INTEREST RATE MODEL 358
16.3 UNCERTAIN CURRENCY MODEL 359
CONTENTS
IX
16.4 BIBLIOGRAPHIC NOTES 363
A PROBABILITY THEORY 365
A.L PROBABILITY MEASURE 365
A.2 RANDOM VARIABLE 369
A.3 PROBABILITY DISTRIBUTION 370
A.4 INDEPENDENCE 372
A.5 OPERATIONAL LAW 373
A.6 EXPECTED VALUE 376
A.7 VARIANCE 382
A.8 MOMENT 386
A.9 ENTROPY 388
A.10 RANDOM SEQUENCE 390
A.11 LAW OF LARGE NUMBERS 395
A.12 CONDITIONAL PROBABILITY 399
A.13 RANDOM SET 401
A. 14 STOCHASTIC PROCESS 403
A.15 STOCHASTIC CALCULUS 405
A.16 STOCHASTIC DIFFERENTIAL EQUATION 406
B CHANCE THEORY 409
B.L CHANCE MEASURE 409
B.2 UNCERTAIN RANDOM VARIABLE 413
B.3 CHANCE DISTRIBUTION 415
B.4 OPERATIONAL LAW 417
B.5 EXPECTED VALUE 424
B.6 VARIANCE 428
B.7 LAW OF LARGE NUMBERS 431
B.8 UNCERTAIN RANDOM PROGRAMMING 433
B.9 UNCERTAIN RANDOM RISK ANALYSIS 436
B.10 UNCERTAIN RANDOM RELIABILITY ANALYSIS 439
B.LL UNCERTAIN RANDOM GRAPH 440
B.12 UNCERTAIN RANDOM NETWORK 444
B.13 UNCERTAIN RANDOM PROCESS 445
B.14 BIBLIOGRAPHIC NOTES 450
C FREQUENTLY ASKED QUESTIONS 453
C.L WHAT IS THE MEANING THAT AN OBJECT FOLLOWS THE LAWS OF PROB
ABILITY THEORY? 453
C.2 WHY DOES FREQUENCY FOLLOW THE LAWS OF PROBABILITY THEORY? . . 454
C.3 WHY IS PROBABILITY THEORY UNABLE TO MODEL BELIEF DEGREE? . . 455
C.4 WHY SHOULD BELIEF DEGREE BE UNDERSTOOD AS AN ODDSMAKER'S
BETTING RATIO RATHER THAN A FAIR ONE? 457
C.5 WHY DOES BELIEF DEGREE FOLLOW THE LAWS OF UNCERTAINTY THEORY? 458
X
CONTENTS
C.6 WHAT IS THE DIFFERENCE BETWEEN PROBABILITY THEORY AND UNCER
TAINTY THEORY? 459
C.7 WHAT GOES WRONG WITH COX'S THEOREM? 459
C.8 WHAT IS THE DIFFERENCE BETWEEN POSSIBILITY THEORY AND UNCER
TAINTY THEORY? 460
C.9 WHY IS FUZZY VARIABLE UNABLE TO MODEL INDETERMINATE QUANTITY? 460
C.10 WHY IS FUZZY SET UNABLE TO MODEL UNSHARP CONCEPT? 461
C.LL DOES THE STOCK PRICE FOLLOW STOCHASTIC DIFFERENTIAL EQUATION OR
UNCERTAIN DIFFERENTIAL EQUATION? 462
C.12 HOW DID "UNCERTAINTY" EVOLVE OVER THE PAST 100 YEARS? . 464
BIBLIOGRAPHY 467
LIST OF FREQUENTLY USED SYMBOLS 483
INDEX 485 |
| any_adam_object | 1 |
| author | Liu, Baoding 1965- |
| author_GND | (DE-588)12374539X |
| author_facet | Liu, Baoding 1965- |
| author_role | aut |
| author_sort | Liu, Baoding 1965- |
| author_variant | b l bl |
| building | Verbundindex |
| bvnumber | BV042226651 |
| classification_rvk | SK 800 ST 300 |
| ctrlnum | (OCoLC)883390902 (DE-599)DNB1053174942 |
| dewey-full | 511 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511 |
| dewey-search | 511 |
| dewey-sort | 3511 |
| dewey-tens | 510 - Mathematics |
| discipline | Maschinenbau / Maschinenwesen Informatik Mathematik |
| edition | Fourth edition |
| format | Book |
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| id | DE-604.BV042226651 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-10T01:31:16Z |
| institution | BVB |
| isbn | 9783662443538 3662443538 9783662443545 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027665045 |
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| physical | xv, 485 Seiten Diagramme |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer uncertainty research |
| spelling | Liu, Baoding 1965- Verfasser (DE-588)12374539X aut Uncertainty theory Baoding Liu Fourth edition Berlin ; Heidelberg ; New York ; Dordrecht ; London Springer [2015] xv, 485 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Springer uncertainty research Frühere Auflagen erschienen in der Springer Serie: "Studies in fuzziness and soft computing" Literaturverzeichnis: Seite 467-482 Ungewissheit (DE-588)4137198-7 gnd rswk-swf Axiomatik (DE-588)4004038-0 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Grobmenge (DE-588)4362502-2 gnd rswk-swf Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Ungewissheit (DE-588)4137198-7 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Axiomatik (DE-588)4004038-0 s Fuzzy-Menge (DE-588)4061868-7 s Grobmenge (DE-588)4362502-2 s X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4704478&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=027665045&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liu, Baoding 1965- Uncertainty theory Ungewissheit (DE-588)4137198-7 gnd Axiomatik (DE-588)4004038-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd Grobmenge (DE-588)4362502-2 gnd Fuzzy-Menge (DE-588)4061868-7 gnd |
| subject_GND | (DE-588)4137198-7 (DE-588)4004038-0 (DE-588)4079013-7 (DE-588)4114528-8 (DE-588)4362502-2 (DE-588)4061868-7 |
| title | Uncertainty theory |
| title_auth | Uncertainty theory |
| title_exact_search | Uncertainty theory |
| title_full | Uncertainty theory Baoding Liu |
| title_fullStr | Uncertainty theory Baoding Liu |
| title_full_unstemmed | Uncertainty theory Baoding Liu |
| title_short | Uncertainty theory |
| title_sort | uncertainty theory |
| topic | Ungewissheit (DE-588)4137198-7 gnd Axiomatik (DE-588)4004038-0 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd Grobmenge (DE-588)4362502-2 gnd Fuzzy-Menge (DE-588)4061868-7 gnd |
| topic_facet | Ungewissheit Axiomatik Wahrscheinlichkeitstheorie Mathematisches Modell Grobmenge Fuzzy-Menge |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4704478&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027665045&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT liubaoding uncertaintytheory |