Advanced concepts in fuzzy logic and systems with membership uncertainty:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Series: | Studies in fuzziness and soft computing
284 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 307 S. zahlr. graph. Darst. |
| ISBN: | 9783642295195 |
Staff View
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
1 U N C E R T A I N T Y IN FUZZY S E T S 1
1.1 FUZZY SETS 1
1.1.1 OPERATIONS ON FUZZY SETS 4
1.2 FUZZY SETS OF TYPE-2 9
1.2.1 INTERVAL-VALUED FUZZY SETS 11
1.2.2 FUZZY-VALUED FUZZY SETS 12
1.3 POSSIBILITY AND NECESSITY MEASURES 13
1.3.1 POSSIBILITY AND NECESSITY MEASURES OF A FUZZY EVENT . . 17 1.4
ROUGH SETS AND THEIR EXTENSIONS 18
1.4.1 ROUGH-FUZZY SETS 21
1.4.2 FUZZY-ROUGH SETS AS A-COMPOSITIONS OF ROUGH-FUZZY SETS 22
1.4.3 FUZZY-ROUGH SETS AS POSSIBILITY AND NECESSITY OF FUZZY SETS 25
1.5 SOURCES OF UNCERTAINTY 27
R E F E R E N C E S 29
2 ALGEBRAIC O P E R A T I O N S O N F U Z Z Y V A L U E D F U Z Z Y S E
T S 33
2.1 SET THEORETIC OPERATIONS WITH THE EXTENSION PRINCIPLE: STATE OF THE
ART 33
2.1.1 OPERATIONS ON INTERVAL-VALUED FUZZY SETS 35
2.1.2 OPERATIONS ON FUZZY-VALUED FUZZY SETS 36
2.2 ANALYTICAL FORMULAE FOR EXTENDED T-NORMS 38
2.2.1 BASIC REMARK FOR FUZZY TRUTH INTERVALS 40
2.2.2 EXTENDED MINIMUM T-NORMS BASED ON ARBITRARY T-NORMS 41
2.2.3 EXTENDED CONTINUOUS TRIANGULAR NORMS BASED ON THE MINIMUM 44
HTTP://D-NB.INFO/1020805382
IMAGE 2
X
CONTENTS
2.2.4 EXTENDED CONTINUOUS T-NORMS BASED ON THE DRASTIC PRODUCT 49
2.2.5 EXTENDED ALGEBRAIC PRODUCT T-NORM BASED ON T H E PRODUCT FOR
TRAPEZOIDAL FUZZY T R U T H INTERVALS 51
2.2.6 EXTENDED LUKASIEWICZ T-NORM BASED ON A CONTINUOUS ARCHIMEDEAN
T-NORM 53
2.3 ANALYTICAL FORMULAE FOR EXTENDED T-CONORMS 58
2.4 APPROXIMATE EXTENDED TRIANGULAR NORMS 61
2.4.1 GAUSSIAN APPROXIMATION TO THE MINIMUM-BASED EXTENDED PRODUCT
T-NORM 62
2.4.2 ASYMMETRIC-GAUSSIAN APPROXIMATIONS T O T H E EXTENDED PRODUCT
BASED ON THE MINIMUM 63
2.5 TRIANGULAR NORMS AND COMPLEMENTARY NORMS ON FUZZY TRUTH VALUES 66
2.6 IMPLICATIONS WITH FUZZY VALUED FUZZY SETS 70
REFERENCES 75
3 DEFUZZIFICATION O F U N C E R T A I N F U Z Z Y S E T S 77
3.1 STATE OF THE A R T OF DEFUZZIFICATION METHODS 77
3.1.1 K M ITERATIVE PROCEDURE FOR INTERVAL EXTENDED DEFUZZIFICATION 79
3.1.2 DEFUZZIFICATION IN CLASSIFICATION 80
3.1.3 APPROXIMATE EXTENDED CENTROID OF INTERVAL-VALUED FUZZY SETS 82
3.2 STATE OF THE A R T OF DEFUZZIFICATION METHODS FOR GENERAL
FUZZY-VALUED FUZZY SETS 85
3.2.1 EXHAUSTIVE EXTENDED CENTROID BASED ON T H E EXTENSION PRINCIPLE 86
3.2.2 EFFICIENT STRATEGY OF TYPE-REDUCTION BASED ON A-PLANES 87
3.2.3 APPROXIMATE EXTENDED CENTROID 89
3.2.4 FINAL DEFUZZIFICATION 90
3.3 CENTROID FOR CONVEX FUZZY-VALUED FUZZY SETS 90
3.3.1 TRAPEZOIDAL FUZZY-VALUED FUZZY SETS 92
3.3.2 TRIANGULAR FUZZY-VALUED FUZZY SETS 99
3.3.3 ASYMMETRIC-GAUSSIAN FUZZY-VALUED FUZZY SETS 103 3.3.4 GAUSSIAN
FUZZY-VALUED FUZZY SETS 113
3.3.5 SYMMETRIC FUZZY-VALUED FUZZY SETS 116
3.4 APPROXIMATE CENTROIDS FOR CONVEX FUZZY-VALUED FUZZY SETS 117
3.4.1 TRIANGULAR AND TRAPEZOIDAL FUZZY-VALUED FUZZY SETS 118
3.4.2 GAUSSIAN FUZZY-VALUED FUZZY SETS 125
IMAGE 3
CONTENTS XI
3.5 COMPARATIVE ANALYSIS 128
3.6 SUMMARY 133
R E F E R E N C E S 134
4 GENERALIZED U N C E R T A I N F U Z Z Y LOGIC S Y S T E M S 137
4.1 STATE OF THE A R T 137
4.1.1 INTERVAL-VALUED APPROXIMATE REASONING 140
4.1.2 FUZZY LOGIC SYSTEMS OF TYPE-2 143
4.2 NOVEL FORMULATIONS OF UNCERTAIN FUZZY LOGIC SYSTEMS 146 4.2.1
INTERVAL FUZZY LOGIC SYSTEMS EMPLOYING FUZZIFICATION 146
4.2.2 GENERAL SYSTEMS BASED ON FUZZY-ROUGH SETS IN T H E SENSE OF
NAKAMURA 160
4.3 PARTICULAR REALIZATIONS OF CONVEX UNCERTAIN FUZZY LOGIC SYSTEMS 168
4.3.1 A TRIANGULAR UNCERTAIN FUZZY LOGIC SYSTEM 169
4.3.2 A TRAPEZOIDAL UNCERTAIN FUZZY LOGIC SYSTEM 171
4.3.3 GAUSSIAN UNCERTAIN FUZZY LOGIC SYSTEMS 173
R E F E R E N C E S 177
5 U N C E R T A I N T Y G E N E R A T I O N IN U N C E R T A I N F U Z Z
Y LOGIC S Y S T E M S 181
5.1 STATE OF THE ART ON UNCERTAINTY GENERATION 181
5.1.1 CONJUNCTIVE AND DISJUNCTIVE NORMAL FORMS 181
5.1.2 INTERVAL FUZZY C-MEANS 182
5.2 MULTIPERSON DECISION MAKING 184
5.2.1 PERCEPTUAL COMPUTING 186
5.2.2 CODING AND COMPUTING WITH WORDS 186
5.2.3 ENCODING RULES 187
5.2.4 TRIANGULAR TYPE-2 AGGREGATION 189
5.2.5 DECODING 192
5.2.6 SIMULATION EXAMPLES 193
5.3 MEMBERSHIP UNCERTAINTY FITTING 201
5.3.1 INTERVAL MEMBERSHIP UNCERTAINTY 202
5.3.2 GENERAL MEMBERSHIP UNCERTAINTY OF TYPE-2 FUZZY SETS 206
5.3.3 SIMULATION EXAMPLES 206
5.4 ROUGH-FUZZY SYSTEMS FOR DISCRETIZATION OF INPUTS AND MISSING
ATTRIBUTES 210
5.4.1 SIMULATION EXAMPLES 210
5.5 GENERALIZED FUZZIFICATION 217
5.5.1 NON-SINGLETON FUZZIFICATION IN POSSIBILISTIC-FUZZY SYSTEMS 219
IMAGE 4
XII CONTENTS
5.5.2 NON-SINGLETON FUZZIFICATION BY THE FUZZY-ROUGH APPROXIMATION 226
5.5.3 SIMULATION EXAMPLES 232
5.5.4 SUMMARY 271
R E F E R E N C E S 274
6 D E S I G N I N G U N C E R T A I N F U Z Z Y LOGIC S Y S T E M S 279
6.1 COMPLETE METHODOLOGY OF DESIGNING UNCERTAIN FUZZY LOGIC SYSTEMS 279
6.1.1 UNCERTAINTY IN FUZZY LOGIC SYSTEMS 280
6.1.2 FUSION OF MULTIPLE SYSTEM DESIGNS 282
6.2 REDUCTION OF COMPUTATIONAL COMPLEXITY 282
6.2.1 APPROXIMATIONS OF INTERVAL-VALUED FUZZY LOGIC SYSTEMS 283
6.2.2 SPECIFICITY OF THE INTERVAL-VALUED APPROACH 299
6.3 SUMMARY 302
R E F E R E N C E S 304
I N D E X 305 |
| any_adam_object | 1 |
| author | Starczewski, Janusz T. |
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| dewey-full | 511.313 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.313 |
| dewey-search | 511.313 |
| dewey-sort | 3511.313 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
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| institution | BVB |
| isbn | 9783642295195 |
| language | English |
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| physical | XII, 307 S. zahlr. graph. Darst. |
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| publisher | Springer |
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| series | Studies in fuzziness and soft computing |
| series2 | Studies in fuzziness and soft computing |
| spelling | Starczewski, Janusz T. Verfasser (DE-588)1026507316 aut Advanced concepts in fuzzy logic and systems with membership uncertainty Janusz T. Starczewski Berlin [u.a.] Springer 2013 XII, 307 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in fuzziness and soft computing 284 Fuzzy-Logik Typ 2 (DE-588)7615986-3 gnd rswk-swf Fuzzy-Logik (DE-588)4341284-1 gnd rswk-swf Fuzzy-Logik (DE-588)4341284-1 s Fuzzy-Logik Typ 2 (DE-588)7615986-3 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-29520-1 Studies in fuzziness and soft computing 284 (DE-604)BV021858135 284 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3994688&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=025375048&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Starczewski, Janusz T. Advanced concepts in fuzzy logic and systems with membership uncertainty Studies in fuzziness and soft computing Fuzzy-Logik Typ 2 (DE-588)7615986-3 gnd Fuzzy-Logik (DE-588)4341284-1 gnd |
| subject_GND | (DE-588)7615986-3 (DE-588)4341284-1 |
| title | Advanced concepts in fuzzy logic and systems with membership uncertainty |
| title_auth | Advanced concepts in fuzzy logic and systems with membership uncertainty |
| title_exact_search | Advanced concepts in fuzzy logic and systems with membership uncertainty |
| title_full | Advanced concepts in fuzzy logic and systems with membership uncertainty Janusz T. Starczewski |
| title_fullStr | Advanced concepts in fuzzy logic and systems with membership uncertainty Janusz T. Starczewski |
| title_full_unstemmed | Advanced concepts in fuzzy logic and systems with membership uncertainty Janusz T. Starczewski |
| title_short | Advanced concepts in fuzzy logic and systems with membership uncertainty |
| title_sort | advanced concepts in fuzzy logic and systems with membership uncertainty |
| topic | Fuzzy-Logik Typ 2 (DE-588)7615986-3 gnd Fuzzy-Logik (DE-588)4341284-1 gnd |
| topic_facet | Fuzzy-Logik Typ 2 Fuzzy-Logik |
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