Approximate reasoning by parts: an introduction to rough mereology
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
2011
|
| Series: | Intelligent systems reference library
20 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XIV, 346 S. graph. Darst. 24 cm |
| ISBN: | 9783642222788 3642222781 |
Staff View
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Record in the Search Index
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IMAGE 1
CONTENTS
ON CONCEPTS. ARISTOTELIAN AND SET-THEORETIC APPROACHES 1
1.1 AN ARISTOTELIAN VIEW ON CONCEPTS 1
1.2 FROM LOCAL TO GLOBAL: SET THEORY 6
1.2.1 NAIVE SET THEORY 7
1.2.2 ALGEBRA OF SETS 7
1.2.3 A FORMAL APPROACH 12
1.3 RELATIONS AND FUNCTIONS 15
1.3.1 ALGEBRA OF RELATIONS 16
1.4 ORDERING RELATIONS 18
1.5 LATTICES AND BOOLEAN ALGEBRAS 21
1.6 INFINITE SETS 22
1.7 WELL-ORDERED SETS 23
1.8 FINITE VERSUS INFINITE SETS 26
1.9 EQUIPOTENCY 28
1.10 COUNTABLE SETS 30
1.11 FILTERS AND IDEALS 31
1.12 EQUIVALENCE RELATIONS 33
1.13 TOLERANCE RELATIONS 35
1.14 A DEEPER INSIGHT INTO LATTICES AND ALGEBRAS 37
REFERENCES 42
TOPOLOGY OF CONCEPTS 45
2.1 METRIC SPACES 45
2.2 PRODUCTS OF METRIC SPACES 50
2.3 COMPACT METRIC SPACES 51
2.4 COMPLETE METRIC SPACES 53
2.5 GENERAL TOPOLOGICAL SPACES 56
2.6 REGULAR OPEN AND REGULAR CLOSED SETS 58
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1012462692
DIGITALISIERT DURCH
IMAGE 2
XII CONTENTS
2.7 COMPACTNESS IN GENERAL SPACES 61
2.8 CONTINUITY 64
2.9 TOPOLOGIES ON SUBSETS 66
2.10 QUOTIENT SPACES 67
2.11 HYPERSPACES 68
2.11.1 TOPOLOGIES ON CLOSED SETS 68
2.12 CECH TOPOLOGIES 73
REFERENCES 77
3 REASONING PATTERNS OF DEDUCTIVE REASONING 79
3.1 THE NATURE OF EXACT REASONING 79
3.2 PROPOSITIONAL CALCULUS 80
3.3 MANY-VALUED CALCULI: 3-VALUED LOGIC OF LUKASIEWICZ 88 3.4
MANY-VALUED CALCULI: N- VALUED LOGIC 96
3.5 MANY-VALUED CALCULI: [0,L]-VALUED LOGICS 99
3.5.1 MV-ALGEBRAS 114
3.6 MANY-VALUED CALCULI: LOGICS OF RESIDUAL IMPLICATIONS . . . 116 3.7
AUTOMATED REASONING 119
3.8 PREDICATE LOGIC 121
3.9 MODAL LOGICS 133
3.9.1 MODAL LOGIC K 133
3.9.2 MODAL LOGIC T 137
3.9.3 MODAL LOGIC S4 138
3.9.4 MODAL LOGIC S5 138
REFERENCES 141
4 REDUCTIVE REASONING ROUGH AND FUZZY SETS AS FRAMEWORKS 145
4.1 ROUGH SET APPROACH MAIN LINES 145
4.2 DECISION SYSTEMS 148
4.3 DECISION RULES 150
4.4 DEPENDENCIES 152
4.5 TOPOLOGY OF ROUGH SETS 153
4.6 A ROUGH SET REASONING SCHEME: THE APPROXIMATE COLLAGE THEOREM 156
4.7 A ROUGH SET SCHEME FOR REASONING ABOUT KNOWLEDGE 158 4.8 FUZZY SET
APPROACH: MAIN LINES 161
4.9 RESIDUAL IMPLICATIONS 168
4.10 TOPOLOGICAL PROPERTIES OF RESIDUAL IMPLICATIONS 169
4.11 EQUIVALENCE AND SIMILARITY IN FUZZY UNIVERSE 175
4.12 INDUCTIVE REASONING: FUZZY DECISION RULES 181
4.13 ON THE NATURE OF REDUCTIVE REASONING 183
REFERENCES 187
IMAGE 3
CONTENTS XIII
5 MEREOLOGY 191
5.1 MEREOLOGY: THE THEORY OF LESNIEWSKI 191
5.2 A MODEM STRUCTURAL ANALYSIS OF MEREOLOGY 199
5.3 MEREOTOPOLOGY 201
5.4 TIMED MEREOLOGY 203
5.5 SPATIO-TEMPORAL REASONING: CELLS 207
5.6 MEREOLOGY BASED ON CONNECTION 209
5.7 CLASSES IN CONNECTION MEREOLOGY 215
5.8 C-QUASI-BOOLEAN ALGEBRA 216
5.9 C-MEREOTOPOLOGY 219
5.10 SPATIAL REASONING: MEREOLOGICAL CALCULI 220
5.10.1 ON REGION CONNECTION CALCULUS 223
REFERENCES 225
6 ROUGH MEREOLOGY 229
6.1 ROUGH INCLUSIONS 230
6.2 ROUGH INCLUSIONS: RESIDUAL MODELS 231
6.3 ROUGH INCLUSIONS: ARCHIMEDEAN MODELS 234
6.4 ROUGH INCLUSIONS: SET MODELS 236
6.5 ROUGH INCLUSIONS: GEOMETRIC MODELS 236
6.6 ROUGH INCLUSIONS: INFORMATION MODELS 237
6.7 ROUGH INCLUSIONS: METRIC MODELS 240
6.8 ROUGH INCLUSIONS: A 3-VALUED ROUGH INCLUSION ON FINITE SETS 240
6.9 SYMMETRIZATION OF ROUGH INCLUSIONS 241
6.10 MEREOGEOMETRY 241
6.11 ROUGH MEREOTOPOLOGY 246
6.11.1 THE CASE OF TRANSITIVE AND SYMMETRIC ROUGH INCLUSIONS 246
6.11.2 THE CASE OF TRANSITIVE NON-SYMMETRIC ROUGH INCLUSIONS 250
6.12 CONNECTIONS FROM ROUGH INCLUSIONS 252
6.12.1 THE CASE OF TRANSITIVE AND SYMMETRIC ROUGH INCLUSIONS 252
6.12.2 THE CASE OF SYMMETRIC NON-TRANSITIVE ROUGH INCLUSIONS AND THE
GENERAL CASE 252
6.13 ROUGH INCLUSIONS AS MANY-VALUED FUZZY EQUIVALENCES . . . 254
REFERENCES 256
7 REASONING WITH ROUGH INCLUSIONS 259
7.1 ON GRANULAR REASONING 259
7.2 ON METHODS FOR GRANULATION OF KNOWLEDGE 261
7.2.1 GRANULES FROM BINARY RELATIONS 261
7.2.2 GRANULES IN INFORMATION SYSTEMS FROM INDISCERNIBILITY 262
IMAGE 4
XIV CONTENTS
7.2.3 GRANULES FROM GENERALIZED DESCRIPTORS 263
7.3 GRANULES FROM ROUGH INCLUSIONS 263
7.4 ROUGH INCLUSIONS ON GRANULES 264
7.5 GENERAL PROPERTIES OF ROUGH MEREOLOGICAL GRANULES 265 7.6 REASONING
BY GRANULAR ROUGH MEREOLOGICAL LOGICS 266 7.7 A LOGIC FOR INFORMATION
SYSTEMS 269
7.7.1 RELATIONS TO MANY-VALUED LOGICS 271
7.8 A GRADED NOTION OF TRUTH 272
7.9 DEPENDENCIES AND DECISION RULES 277
7.10 AN APPLICATION TO CALCULUS OF PERCEPTIONS 278
7.11 MODAL ASPECTS OF ROUGH MEREOLOGICAL LOGICS 280
7.11.1 A MODAL LOGIC WITH INGREDIENT ACCESSIBILITY 281 7.11.2 MODAL
LOGIC OF ROUGH SET APPROXIMATIONS 282 7.12 REASONING IN MULTI-AGENT AND
DISTRIBUTED SYSTEMS 283 7.13 REASONING IN COGNITIVE SCHEMES 288
7.13.1 ROUGH MEREOLOGICAL PERCEPTRON 290
REFERENCES 292
8 REASONING BY ROUGH MEREOLOGY IN PROBLEMS OF BEHAVIORAL ROBOTICS 297
8.1 PLANNING OF ROBOT MOTION 297
8.2 POTENTIAL FIELDS FROM ROUGH INCLUSIONS 300
8.3 PLANNING FOR TEAMS OF ROBOTS 303
8.4 ROUGH MEREOLOGICAL APPROACH TO ROBOT FORMATIONS 308 REFERENCES 315
9 ROUGH MEREOLOGICAL CALCULUS OF GRANULES 319
9.1 ON DECISION RULES 319
9.2 THE IDEA OF GRANULAR ROUGH MEREOLOGICAL CLASSIFIERS 322 9.3
CLASSIFICATION BY GRANULES OF TRAINING OBJECTS 324
9.4 A TREATMENT OF MISSING VALUES 326
9.5 GRANULAR ROUGH MEREOLOGICAL CLASSIFIERS USING RESIDUALS . 329 9.6
GRANULAR ROUGH MEREOLOGICAL CLASSIFIERS WITH MODIFIED VOTING PARAMETERS
331
REFERENCES 333
AUTHOR INDEX 335
TERM INDEX 341 |
| any_adam_object | 1 |
| author | Polkowski, Lech 1946- |
| author_GND | (DE-588)120167204 |
| author_facet | Polkowski, Lech 1946- |
| author_role | aut |
| author_sort | Polkowski, Lech 1946- |
| author_variant | l p lp |
| building | Verbundindex |
| bvnumber | BV039682420 |
| classification_rvk | ST 301 |
| ctrlnum | (OCoLC)733249509 (DE-599)DNB1012462692 |
| dewey-full | 006.333 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 006 - Special computer methods |
| dewey-raw | 006.333 |
| dewey-search | 006.333 |
| dewey-sort | 16.333 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| language | English |
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| publishDate | 2011 |
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| spelling | Polkowski, Lech 1946- Verfasser (DE-588)120167204 aut Approximate reasoning by parts an introduction to rough mereology Lech Polkowski Berlin ; Heidelberg Springer 2011 XIV, 346 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Intelligent systems reference library 20 Literaturangaben Approximatives Schließen (DE-588)4231005-2 gnd rswk-swf Grobmenge (DE-588)4362502-2 gnd rswk-swf Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Mengenlehre (DE-588)4074715-3 gnd rswk-swf Approximatives Schließen (DE-588)4231005-2 s Mengenlehre (DE-588)4074715-3 s Fuzzy-Menge (DE-588)4061868-7 s Grobmenge (DE-588)4362502-2 s DE-604 Erscheint auch als Online-Ausgabe Approximate Reasoning by Parts Intelligent systems reference library 20 (DE-604)BV035704685 20 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3835641&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=024531393&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Polkowski, Lech 1946- Approximate reasoning by parts an introduction to rough mereology Intelligent systems reference library Approximatives Schließen (DE-588)4231005-2 gnd Grobmenge (DE-588)4362502-2 gnd Fuzzy-Menge (DE-588)4061868-7 gnd Mengenlehre (DE-588)4074715-3 gnd |
| subject_GND | (DE-588)4231005-2 (DE-588)4362502-2 (DE-588)4061868-7 (DE-588)4074715-3 |
| title | Approximate reasoning by parts an introduction to rough mereology |
| title_auth | Approximate reasoning by parts an introduction to rough mereology |
| title_exact_search | Approximate reasoning by parts an introduction to rough mereology |
| title_full | Approximate reasoning by parts an introduction to rough mereology Lech Polkowski |
| title_fullStr | Approximate reasoning by parts an introduction to rough mereology Lech Polkowski |
| title_full_unstemmed | Approximate reasoning by parts an introduction to rough mereology Lech Polkowski |
| title_short | Approximate reasoning by parts |
| title_sort | approximate reasoning by parts an introduction to rough mereology |
| title_sub | an introduction to rough mereology |
| topic | Approximatives Schließen (DE-588)4231005-2 gnd Grobmenge (DE-588)4362502-2 gnd Fuzzy-Menge (DE-588)4061868-7 gnd Mengenlehre (DE-588)4074715-3 gnd |
| topic_facet | Approximatives Schließen Grobmenge Fuzzy-Menge Mengenlehre |
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