On intuitionistic fuzzy sets theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2012
|
| Schriftenreihe: | Studies in fuzziness and soft computing
283 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XI, 323 S. graph. Darst. |
| ISBN: | 9783642291265 3642291260 9783642291272 |
Internformat
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| 100 | 1 | |a Atanasov, Krasimir T. |d 1954- |e Verfasser |0 (DE-588)121283259 |4 aut | |
| 245 | 1 | 0 | |a On intuitionistic fuzzy sets theory |c Krassimir T. Atanassov |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2012 | |
| 300 | |a XI, 323 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
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Datensatz im Suchindex
| _version_ | 1805146860417974272 |
|---|---|
| adam_text |
IMAGE 1
C O N T E N T S
1 O N T H E C O N C E P T O F I F S S 1
1.1 DEFINITION OF THE CONCEPT OF IFS 1
1.2 FIRST EXAMPLE 2
1.3 SOME COMMENTS ON THE CONCEPT OF IFS 3
1.4 FIRST EXAMPLE FROM NUMBER THEORY 6
1.5 AN EXAMPLE RELATED TO THE GAME OF CHESS 7
1.6 SOME WAYS FOR ALTERING THE EXPERTS'ESTIMATIONS 12
2 O P E R A T I O N S A N D R E L A T I O N S OVER I F S S 17
2.1 BASIC OPERATIONS AND RELATIONS OVER IFSS 17
2.2 SHORT REMARKS ON INTUITIONISTIC FUZZY LOGICS. P A R T 1 23
2.3 SECOND EXAMPLE FROM AREA OF NUMBER THEORY 23
2.4 OTHER OPERATIONS OVER IFSS 26
2.5 ON THE DIFFERENCE BETWEEN CRISP SETS AND IFSS 30
2.6 INTUITIONISTIC FUZZY TAUTOLOGICAL SETS 32
3 G E O M E T R I C A L INTERPRETATIONS O F I F S S 37
3.1 GEOMETRICAL INTERPRETATIONS OF AN IFS 37
3.2 GEOMETRICAL INTERPRETATIONS OF OPERATIONS 39
3.3 OTHER GEOMETRICAL INTERPRETATIONS OF THE IFSS 42
3.4 ON IF-INTERPRETATION OF INTERVAL D A T A 44
3.5 ON SOME TRANSFORMATION FORMULAE 45
, 3.6 PROPERTY OF THE IFS-INTERPRETATIONAL TRIANGLE 46
3.7 OTHER WAYS FOR ALTERING EXPERTS'ESTIMATIONS 49
3.8 AN EXAMPLE: IFSS AND COMPLEX ANALYSIS 50
4 M O D A L A N D TOPOLOGICAL O P E R A T O R S 53
4.1 "NECESSITY" AND "POSSIBILITY" OPERATORS 53
4.2 TOPOLOGICAL OPERATORS OVER IFSS 56
. 4.3 EXTENDED TOPOLOGICAL OPERATORS 60
4.4 WEIGHT-CENTER OPERATOR 64
HTTP://D-NB.INFO/1020436190
IMAGE 2
X CONTENTS
4.5 OTHER EXTENDED TOPOLOGICAL OPERATORS 65
4.6 SHORT REMARKS ON INTUITIONISTIC FUZZY LOGICS. P A R T 2 69
4.7 AN EXAMPLE: IF-INTERPRETATIONS OF CONWAY'S GAME OF LIFE. P A R T 1
70
4.7.1 IF-CRITERIA OF EXISTING, BIRTH AND DEATH OF AN ASTERISK 70 4.7.2
IF-RULES FOR CHANGING THE GAME-FIELD 72
4.7.3 TRANSFORMATIONS OF THE GAME FIELD BY STANDARD TOPOLOGICAL
OPERATORS 74
4.7.4 TRANSFORMATIONS OF THE GAME FIELD BY EXTENDED TOPOLOGICAL
OPERATORS 75
5 E X T E N D E D M O D A L O P E R A T O R S 77
5.1 OPERATORS D A A N D F Q I / G 77
5.2 SHORT REMARKS ON INTUITIONISTIC FUZZY LOGICS. P A R T 3 81
5.3 OPERATOR G A ,@ 82
5.4 OPERATORS H A;/3 , H * ^ , J ^ , AND J* :/3 83
5.5 AN EXAMPLE: IF-INTERPRETATIONS OF CONWAY'S GAME OF LIFE. P A R T 2
87
5.5.1 GLOBAL TRANSFORMATIONS OF THE GAME FIELD BY MODAL AND EXTENDED
MODAL OPERATORS 87
5.5.2 LOCAL TRANSFORMATIONS OF THE GAME FIELD BY MODAL AND EXTENDED
MODAL OPERATORS 87
5.6 RELATIONS BETWEEN OPERATORS 89
5.7 OPERATOR X 0 ,6 C RF E ,/ 97
5.8 EXTENDED MODAL OPERATORS FOR NEGATION 100
5.9 OPERATOR X A ,B,C,D,E,F 107
5.10 PARTIAL EXTENSION OF THE EXTENDED MODAL OPERATORS 109
6 O T H E R T Y P E S O F O P E R A T O R S 113
6.1 IFSS OF CERTAIN LEVEL 113
6.2 LEVEL TYPE OF OPERATORS 117
6.3 OTHER TYPES OF MODAL OPERATORS 121
6.4 RELATIONS BETWEEN THE MOST GENERAL IF-MODAL OPERATORS . . . . 128
7 N O R M S A N D M E T R I C S OVER I F S S 133
7.1 STANDARD IF-NORMS AND METRICS 133
7.2 CANTOR'S IF-NORMS 139
7.3 INTUITIONISTIC FUZZY HISTOGRAMS 140
8 INTUITIONISTIC F U Z Z Y R E L A T I O N S ( I F R S ) 147
8.1 CARTESIAN PRODUCTS OVER IFSS 147
8.2 INDEX MATRIX 150
8.2.1 BASIC DEFINITIONS AND PROPERTIES 150
8.2.2 OTHER DEFINITIONS AND PROPERTIES 153
8.2.3 INTUITIONISTIC FUZZY IMS (IFIMS) 162
8.3 INTUITIONISTIC FUZZY RELATIONS (IFRS) 165
IMAGE 3
CONTENTS XI
8.4 INTUITIONISTIC FUZZY GRAPHS (IFGS) 167
8.5 EXAMPLE 180
8.5.1 EXPERTS WHO ORDER ALTERNATIVES 182
8.5.2 MEASUREMENT TOOLS T H A T EVALUATE ALTERNATIVES 186
8.6 SOME WAYS OF DETERMINING MEMBERSHIP AND NONMEMBERSHIP FUNCTIONS 190
9 N E W INTUITIONISTIC F U Z Z Y O P E R A T I O N S 195
9.1 REMARKS ON IFL. P A R T 4 195
9.1.1 DEFINITIONS AND PROPERTIES OF SOME INTUITIONISTIC FUZZY
IMPLICATIONS AND NEGATIONS 196
9.1.2 ON LAW OF EXCLUDED MIDDLE AND ITS MODIFICATIONS . . . . 204 9.1.3
ON DE MORGAN'S LAWS AND THEIR MODIFICATIONS 205
9.1.4 ON THE AXIOMS OF PROPOSITIONAL INTUITIONISTIC LOGIC . . . 206
9.1.5 A NEW ARGUMENT T H A T THE INTUITIONISTIC FUZZY SETS HAVE
INTUITIONISTIC NATURE 208
9.2 IF IMPLICATIONS AND NEGATIONS OVER IFSS 208
9.2.1 DEFINITIONS AND PROPERTIES OF I F IMPLICATIONS AND NEGATIONS 208
9.2.2 ON ONE OF BACZYNSKI-JAYARAM'S PROBLEMS 225
9.2.3 IF NEGATIONS AND THE OPERATORS OVER IFSS 230
9.3 DEFINITIONS AND PROPERTIES OF SOME I F SUBTRACTIONS 236
9.4 (E. '/^-NEGATIONS, IMPLICATIONS, SUBTRACTIONS, NORMS AND DISTANCES
243
9.5 CONCLUDING REMARKS 257
10 O N T W O N E W E X T E N S I O N S O F INTUITIONISTIC F U Z Z Y S E
T S 259
10.1 ON SOME INTUITIONISTIC FUZZY EXTENSIONS 259
10.2 TEMPORAL IFSS 260
10.3 EXAMPLE: AN IF-INTERPRETATION OF RGB-COLOUR SYSTEM 264 10.4 I F
MULTIDIMENSIONAL SETS 266
11 C O N C L U D I N G R E M A R K S 273
11.1 THE INTUITIONISTIC FUZZY SETS AS CONSTRUCTIVE OBJECTS 273
11.2 ON SOME OPEN AND SOLVED PROBLEMS 280
REFERENCES' 285
I N D E X 321 |
| any_adam_object | 1 |
| author | Atanasov, Krasimir T. 1954- |
| author_GND | (DE-588)121283259 |
| author_facet | Atanasov, Krasimir T. 1954- |
| author_role | aut |
| author_sort | Atanasov, Krasimir T. 1954- |
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| building | Verbundindex |
| bvnumber | BV040267844 |
| classification_rvk | ST 301 |
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| dewey-full | 511.3223 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3223 |
| dewey-search | 511.3223 |
| dewey-sort | 3511.3223 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-21T00:36:38Z |
| institution | BVB |
| isbn | 9783642291265 3642291260 9783642291272 |
| language | English |
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| physical | XI, 323 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
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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 | Atanasov, Krasimir T. 1954- Verfasser (DE-588)121283259 aut On intuitionistic fuzzy sets theory Krassimir T. Atanassov Berlin [u.a.] Springer 2012 XI, 323 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in fuzziness and soft computing 283 Intuitionistische Logik (DE-588)4162199-2 gnd rswk-swf Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Fuzzy-Menge (DE-588)4061868-7 s Intuitionistische Logik (DE-588)4162199-2 s DE-604 Studies in fuzziness and soft computing 283 (DE-604)BV021858135 283 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3989309&prov=M&dok%5Fvar=1&dok%5Fext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025123478&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Atanasov, Krasimir T. 1954- On intuitionistic fuzzy sets theory Studies in fuzziness and soft computing Intuitionistische Logik (DE-588)4162199-2 gnd Fuzzy-Menge (DE-588)4061868-7 gnd |
| subject_GND | (DE-588)4162199-2 (DE-588)4061868-7 |
| title | On intuitionistic fuzzy sets theory |
| title_auth | On intuitionistic fuzzy sets theory |
| title_exact_search | On intuitionistic fuzzy sets theory |
| title_full | On intuitionistic fuzzy sets theory Krassimir T. Atanassov |
| title_fullStr | On intuitionistic fuzzy sets theory Krassimir T. Atanassov |
| title_full_unstemmed | On intuitionistic fuzzy sets theory Krassimir T. Atanassov |
| title_short | On intuitionistic fuzzy sets theory |
| title_sort | on intuitionistic fuzzy sets theory |
| topic | Intuitionistische Logik (DE-588)4162199-2 gnd Fuzzy-Menge (DE-588)4061868-7 gnd |
| topic_facet | Intuitionistische Logik Fuzzy-Menge |
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