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Uncertainty theory: a branch of mathematics for modeling human uncertainty

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Bibliographic Details
Main Author:	Liu, Baoding 1965- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2010
Series:	Studies in computational intelligence 300
Subjects:	Ungewissheit Mathematik
Online Access:	Inhaltstext Inhaltsverzeichnis
Physical Description:	XI, 350 S. graph. Darst.
ISBN:	9783642139581

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MARC


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Record in the Search Index

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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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author	Liu, Baoding 1965-
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discipline	Maschinenbau / Maschinenwesen Informatik Mathematik
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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
url	http://deposit.dnb.de/cgi-bin/dokserv?id=3480863&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=025193972&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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