Fuzzy classifiers and their relation to cluster analysis and neural networks:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin
Logos-Verl.
2011
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 202 S. graph. Darst. 25 cm |
| ISBN: | 9783832514631 3832514635 |
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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 INTRODUCTION 9
2 FUZZY CLASSIFIERS 15
2.1 DESCRIPTION OF FUZZY CLASSIFIERS 15
2.1.1 FUZZY SETS 15
2.1.2 FUZZY CLASSIFICATION SYSTEMS 18
2.2 EXAMPLES FOR DIFFERENT T-NORMS 21
2.3 ADVANTAGES OF FUZZY CLASSIFIERS 23
3 FUZZY MAX-MIN CLASSIFIERS 25
3.1 FUZZY MAX-MIN CLASSIFICATION SYSTEMS 26
3.2 BASIC DEFINITIONS 29
3.3 A POINT WITH ONLY TWO RELEVANT VARIABLES 33
3.3.1 FIRST CASE: ONE DOMINATING VARIABLE FOR EACH RULE . . 33 3.3.2
SECOND CASE: RULES WITH MORE THAN ONE DOMINATING VARIABLE 37
3.4 GEOMETRIC CHARACTERISTICS OF THE MIN-T-NORM 39
3.5 CONSEQUENCES 40
4 FCS W I T H LUKASIEWICZ-T-NORM 4 3
4.1 FUZZY CLASSIFICATION WITH LUKASIEWICZ-T-NORM 44
4.2 PIECEWISE LINEAR SEPARATION LINES 45
4.3 TREATMENT OF THE ACUTE ANGLE 50
4.3.1 FIRST POSSIBILITY: NEGLIGIBLE SMALL RECTANGLE 51
4.3.2 SECOND POSSIBILITY: USING UNCOMMON RULES 52
4.3.3 GENERALIZATION FOR THE ACUTE ANGLE 57
4.4 IMPROPER SEPARATION LINES 57
4.5 CONSEQUENCES 58
5 GEOMETRIC CHARACTERIZATION 5 9
5.1 BASIC REQUIREMENTS 59
5
HTTP://D-NB.INFO/982565747
IMAGE 2
6 CONTENTS
5.2 OVERLAP OF FUZZY SETS 60
5.3 SEVERAL RULES INSIDE A SINGLE CUBOID 68
5.4 SEPARATION FOR THE WHOLE DATA SPACE 70
5.5 CONSEQUENCES 72
6 FUZZY CLUSTERING 7 3
6.1 FUZZY CLASSIFICATION SYSTEMS 73
6.1.1 FUZZY CLASSIFIERS 73
6.1.2 FUZZY CLUSTERING 75
6.2 HYPERPLANES AND CUBOIDS 80
6.3 COMPLEMENTARY REMARKS 84
7 CLASSIFICATION RULES FROM CLUSTERS 8 5
7.1 H HYPERPLANES 86
7.1.1 THREE-DIMENSIONS EXAMPLES 87
7.1.2 BASIC PRINCIPLES 89
7.1.3 STEPS FOR THE CONSTRUCTION OF THE CLASSIFICATION SYSTEM 91 7.2
SEGMENTATION INTO CUBOIDS 101
7.2.1 REGULAR GRID 101
7.2.2 AS FEW CUBOIDS AS POSSIBLE 102
7.3 AN EXAMPLE: THE IRIS DATA SET 103
7.4 CONCLUSIONS 106
8 PERCEPTRONS AND M L P S 107
8.1 THE PERCEPTRON 108
8.2 LINEARLY SEPARABLE PROBLEM 110
8.3 THE MULTILAYER PERCEPTRON 112
9 CONSTRUCTION O F AN M L P 115
9.1 SUPPOSITIONS 117
9.2 MLP FROM GIVEN HYPERPLANES 118
9.2.1 THETOGICAL AND 118
9.2.2 THE LOGICAL OR 119
9.2.3 USING - 1 AND 1 INSTEAD OF 0 AND 1 120
9.3 DISJUNCTIVE NORMAL FORM 122
9.4 CONJUNCTIVE NORMAL FORM 123
9.5 USING A SIGMOIDAL ACTIVATION FUNCTION 124
9.6 MLP FROM CLUSTERING 125
9.7 MLP FOR IRIS DATA SET 131
9.7.1 DETERMINING THE HYPERPLANES 131
9.7.2 SIMPLIFYING THE MULTILAYER PERCEPTRON 134
IMAGE 3
CONTENTS 7
9.8 FURTHER CONSIDERATIONS 138
10 APPLICATION: WEATHER D A T A 141
10.1 THE DATASET 142
10.1.1 PREPARING THE DATA 143
10.1.2 THE CLUSTERING 144
10.1.3 CONSTRUCTION OF THE MLP 144
10.1.4 DETERMINING THE WEIGHTS FOR A CONTINUOUS OUTPUT . . . . 145 10.2
THE RESULTS 146
10.3 UNINITIALIZED MULTILAYER PERCEPTRONS 150
10.4 CONCLUSION AND OUTLOOK 151
11 CONCLUSIONS AND FUTURE PERSPECTIVES 153
A T H E TAYLOR EXPANSION RESTRICTION 155
B T H E ALGORITHMS 159
B.L RULES WITH LUK-T-NORM 159
B.2 CLASSIFICATION RULES FROM FUZZY CLUSTERS 163
B.3 CALCULATING MLP FROM FUZZY CLUSTERS 169
B.4 MLP WITH CONTINUOUS OUTPUT 173
C ANALYSIS O F T H E WEATHER DATA 175
C.L THE PROTOTYPES OF THE CLUSTERING 175
LIST O F FIGURES 179
LIST O F TABLES 181
SYMBOLS 185
ABBREVIATIONS 187
ALGORITHMS 189
BIBLIOGRAPHY 191
|
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| author_facet | Schmidt, Birka von |
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| ctrlnum | (OCoLC)816277398 (DE-599)DNB982565747 |
| dewey-full | 006.3 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 006 - Special computer methods |
| dewey-raw | 006.3 |
| dewey-search | 006.3 |
| dewey-sort | 16.3 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Thesis Book |
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| id | DE-604.BV040491819 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:24:54Z |
| institution | BVB |
| isbn | 9783832514631 3832514635 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025338792 |
| oclc_num | 816277398 |
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| physical | 202 S. graph. Darst. 25 cm |
| publishDate | 2011 |
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| publisher | Logos-Verl. |
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| spelling | Schmidt, Birka von Verfasser aut Fuzzy classifiers and their relation to cluster analysis and neural networks Birka von Schmidt Berlin Logos-Verl. 2011 202 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Zugl.: Braunschweig, Techn. Univ., Diss., 2005 Mehrschichten-Perzeptron (DE-588)4354626-2 gnd rswk-swf Fuzzy-Regelsystem (DE-588)4728095-5 gnd rswk-swf Fuzzy-Clusteranalyse (DE-588)4802783-2 gnd rswk-swf Automatische Klassifikation (DE-588)4120957-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Automatische Klassifikation (DE-588)4120957-6 s Fuzzy-Regelsystem (DE-588)4728095-5 s Fuzzy-Clusteranalyse (DE-588)4802783-2 s Mehrschichten-Perzeptron (DE-588)4354626-2 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025338792&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schmidt, Birka von Fuzzy classifiers and their relation to cluster analysis and neural networks Mehrschichten-Perzeptron (DE-588)4354626-2 gnd Fuzzy-Regelsystem (DE-588)4728095-5 gnd Fuzzy-Clusteranalyse (DE-588)4802783-2 gnd Automatische Klassifikation (DE-588)4120957-6 gnd |
| subject_GND | (DE-588)4354626-2 (DE-588)4728095-5 (DE-588)4802783-2 (DE-588)4120957-6 (DE-588)4113937-9 |
| title | Fuzzy classifiers and their relation to cluster analysis and neural networks |
| title_auth | Fuzzy classifiers and their relation to cluster analysis and neural networks |
| title_exact_search | Fuzzy classifiers and their relation to cluster analysis and neural networks |
| title_full | Fuzzy classifiers and their relation to cluster analysis and neural networks Birka von Schmidt |
| title_fullStr | Fuzzy classifiers and their relation to cluster analysis and neural networks Birka von Schmidt |
| title_full_unstemmed | Fuzzy classifiers and their relation to cluster analysis and neural networks Birka von Schmidt |
| title_short | Fuzzy classifiers and their relation to cluster analysis and neural networks |
| title_sort | fuzzy classifiers and their relation to cluster analysis and neural networks |
| topic | Mehrschichten-Perzeptron (DE-588)4354626-2 gnd Fuzzy-Regelsystem (DE-588)4728095-5 gnd Fuzzy-Clusteranalyse (DE-588)4802783-2 gnd Automatische Klassifikation (DE-588)4120957-6 gnd |
| topic_facet | Mehrschichten-Perzeptron Fuzzy-Regelsystem Fuzzy-Clusteranalyse Automatische Klassifikation Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025338792&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schmidtbirkavon fuzzyclassifiersandtheirrelationtoclusteranalysisandneuralnetworks |