Fuzzy sets, fuzzy logic, fuzzy methods: with applications
Continuing research in fuzzy theory has dramatically developed the field of intelligent systems. Presenting a highly accessible introduction to this most topical area, this title provides a comprehensive understanding of fuzzy sets and their applications. A range of carefully selected topics, from f...
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Chichester u.a.
Wiley
1995
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Continuing research in fuzzy theory has dramatically developed the field of intelligent systems. Presenting a highly accessible introduction to this most topical area, this title provides a comprehensive understanding of fuzzy sets and their applications. A range of carefully selected topics, from fuzzy arithmetic and fuzzy programming through to qualitative and quantitative fuzzy data analysis, are discussed in detail, giving a strong framework for addressing the various applications of fuzzy sets. Features include clear explanation of the mathematical basis of fuzzy set theory, comprehensive coverage of principles and their applications, and presentation of a wide range of practical applications The growing applications of fuzzy theory ensures this book will appeal to both communication and control engineering professionals with a general background in mathematics. Computer scientists and researchers, as well as applied mathematicians, will find this an invaluable reference source providing information on current research topics |
| Physical Description: | X, 239 S. |
| ISBN: | 0471956368 |
Staff View
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| 520 | 3 | |a Continuing research in fuzzy theory has dramatically developed the field of intelligent systems. Presenting a highly accessible introduction to this most topical area, this title provides a comprehensive understanding of fuzzy sets and their applications. A range of carefully selected topics, from fuzzy arithmetic and fuzzy programming through to qualitative and quantitative fuzzy data analysis, are discussed in detail, giving a strong framework for addressing the various applications of fuzzy sets. Features include clear explanation of the mathematical basis of fuzzy set theory, comprehensive coverage of principles and their applications, and presentation of a wide range of practical applications | |
| 520 | |a The growing applications of fuzzy theory ensures this book will appeal to both communication and control engineering professionals with a general background in mathematics. Computer scientists and researchers, as well as applied mathematicians, will find this an invaluable reference source providing information on current research topics | ||
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Record in the Search Index
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| adam_text | FUZZY SETS, FUZZY LOGIC FUZZY METHODS WITH APPLICATIONS HANS BANDEMER TU
BERGAKADEMIE FREIBERG, GERMANY SIEGFRIED GOTTWALD UNIVERSITAET LEIPZIG,
GERMANY JOHN WILEY & SONS CHICHESTER * NEW YORK * BRISBANE * TORONTO *
SINGAPORE CONTENTS PREFACE IX 1 INTRODUCTION 1 1.1 WHY FUZZY SETS? 1 1.2
DEVELOPMENT OF THEORY AND APPLICATIONS 5 2 FUZZY SETS 9 2.1 BASIC
NOTIONS 9 2.1.1 MEMBERSHIP FUNCTIONS OF FUZZY SETS 9 2.1.2
CHARACTERISTIC VALUES OF FUZZY SETS 11 2.1.3 INCLUSION FOR FUZZY SETS 14
)( 2.1.4 FUZZY SETS AND MANY-VALUED LOGIC* 15 2.2 EXAMPLES FOR FUZZY
SETS AND THEIR SPECIFICATION 18 2.2.1 SPECIFYING MEMBERSHIP FUNCTION
TYPES 18 2.2.2 FUZZY POINTS AND FUZZY REGIONS 21 2.2.3 FUZZY RELATIONS
23 X 2.2.4 FUZZY MAPPINGS AND FUZZY FUNCTIONS 25 2.2.5 THE DETERMINATION
OF MEMBERSHIP FUNCTIONS 27 2.3 OPERATIONS WITH FUZZY SETS 28 2.3.1 BASIC
SET ALGEBRAIC OPERATIONS 28 2.3.2 FURTHER VARIANTS OF INTERSECTIONS AND
UNIONS 32 2.3.3 EXTENDING POINT OPERATIONS TO FUZZY SETS 35 2.4
GENERALISED, T-NORM-BASED OPERATIONS 36 2.4.1 A GENERAL CLASS OF SET
ALGEBRAIC OPERATIONS 36 2.4.2 SPECIAL CLASSES OF T-NORMS 42 2.4.3 A
MODEL THEORETIC VIEW ON GENERAL SET ALGEBRAIC OPERATIONS* 45 VI CONTENTS
2.5 FUZZY NUMBERS AND THEIR ARITHMETIC 48 2.5.1 FUZZY NUMBERS AND FUZZY
INTERVALS 48 2.5.2 ARITHMETIC OPERATIONS 49 2.5.3 FUZZY NUMBERS OF
RESTRICTED SHAPE AND THEIR REPRESENTATION 54 2.5.4 INTEGRATING FUZZY
FUNCTIONS 59 K 3 FUZZIFIED RELAT IONSHIPS 61 3.1 FUZZY RELATIONS 61
3.1.1 BASIC NOTIONS AND OPERATIONS 61 3.1.2 T-NORM BASED OPERATIONS 64
3.1.3 PROJECTIONS AND CYLINDRIFICATIONS 66 3.2 PROPERTIES OF FUZZY
RELATIONS 68 3.2.1 BASIC RELATIONAL PROPERTIES 68 3.2.2 A DESCRIPTION OF
DISTANCES OF FUZZY SETS* 70 3.2.3 FUZZY EQUIVALENCE RELATIONS 72 3.2.4
FUZZY ORDERING RELATIONS* 74 3.2.5 TOWARD FUZZIFIED RELATION PROPERTIES*
75 3.3 FUZZY RELATIONSHIPS BETWEEN VARIABLES 76 3.3.1 FUZZILY RELATED
VARIABLES 76 3^3.2 THE POSSIBILITY INTERPRETATION OF FUZZY SETS 78 3.3.3
FUZZY VARIABLES AND FUZZY IMPLICATIONS 80 3.4 FUZZY PROGRAMMING 82 3.4.1
FUZZY OBJECTIVES AND CONSTRAINTS 82 3.4.2 OPTIMISING OVER A FUZZY REGION
86 4 LINGUISTIC VARIABLES AND THEIR APPLICATIONS 89 4.1 THE NOTION OF A
LINGUISTIC VARIABLE 89 4.2 FUZZY CONTROL 93 4.2.1 FUZZY CONTROLLER 93
4.2.2 THE MAMDANI APPROACH 96 4.2.3 THE METHOD OF ACTIVATION DEGREES 99
4.2.4 COMPARING BOTH APPROACHES* 100 4.2.5 THE PROBLEM OF
DEFUZZIFICATION 102 4.2.6 THE SUGENO APPROACH 106 4.3 RELATIONAL
EQUATIONS AND FUZZY CONTROL 107 4.3.1 SOLUTIONS OF SYSTEMS OF RELATIONAL
EQUATIONS 107 4.3.2 APPROXIMATE SOLUTIONS AND THEIR EVALUATION 110
CONTENTS V]] 4.4 APPROXIMATE REASONING 115 4.4.1 THE GENERAL IDEA 115
4.4.2 RULES FOR MODIFIKATION 117 4.4.3 RULES FOR COMPOSITION 118 4.4.4
RULES FOR QUANTIFICATION 120 4.4.5 RULES FOR QUALIFICATION 123 4.5
EXAMPLES FOR APPLICATIONS OF LINGUISTIC VARIABLES AND OF FUZZY
CONTROLLERS 127 MEASURE THEORY AND FUZZY SETS 133 5.1 FUZZY MEASURES FOR
CRISP SETS 133 5.1.1 FUZZY MEASURES 133 5.1.2 POSSIBILITY AND NECESSITY
MEASURES 136 5.1.3 SUGENO MEASURES 139 5.1.4 DEMPSTER - SHAFER THEORY
139 5.2 FUZZY MEASURES FOR FUZZY SETS 143 5.2.1 PROBABILITY FOR FUZZY
SETS 144 5.2.2 POSSIBILITY FOR FUZZY SETS 146 5.2.3 FUZZY INTEGRALS 147
5.2.4 CREDIBILITY FOR FUZZY SETS 150 5.3 FUZZINESS AND PROBABILITY 152
5.3.1 PROBABILISTIC SETS 152 5.3.2 FUZZY PROBABILITY 152 5.3.3 RANDOM
FUZZY SETS 155 5.3.4 STATISTICS FOR FUZZY OBSERVATIONS OF RANDOM
VARIABLES 157 5.4 SOME APPLICATIONS 158 5.4.1 COMBINING FUZZY KNOWLEDGE
159 5.4.2 FUZZY DECISION THEORY 161 5.4.3 FUZZY STATISTICS 164 5.5
FUZZINESS MEASURES 165 5.5.1 ENTROPY MEASURES 165 5.5.2 ENERGY MEASURES
168 5.5.3 OTHER SUGGESTIONS 169 FUZZY DATA ANALYSIS 173 6.1 DATA AND
THEIR ANALYSIS 173 6.2 QUALITATIVE DATA ANALYSIS 177 6.2.1 FUZZY CLUSTER
ANALYSIS OF CRISP DATA 177 6.2.2 ARRANGEMENTS OF FUZZY DATA USING THEIR
SIMILARITY 182 6.2.3 SOME PRACTICAL EXAMPLES USING SIMILARITY 189 VLLL
CONTENTS 6.3 QUANTITATIVE DATA ANALYSIS 196 6.3.1 PRELIMINARY
EXPLORATORY ANALYSIS 197 6.3.2 EVALUATING FUNCTIONAL RELATIONSHIPS 199
6.3.3 APPROXIMATION OF OR BY FUNCTIONAL RELATIONSHIPS 202 6.3.4 OTHER
PROBLEMS OF FUZZY INFERENCE 204 6.3.5 SEQUENTIAL OPTIMISATION OF
FUZZIFYING FUNCTIONS 207 6.4 EVALUATION OF METHODS IN FUZZY DATA
ANALYSIS 209 BIBLIOGRAPHY 217 INDEX 235
|
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| spelling | Bandemer, Hans 1932-2009 Verfasser (DE-588)115503897 aut Fuzzy sets, fuzzy logic, fuzzy methods with applications Hans Bandemer ; Siegfried Gottwald Chichester u.a. Wiley 1995 X, 239 S. txt rdacontent n rdamedia nc rdacarrier Continuing research in fuzzy theory has dramatically developed the field of intelligent systems. Presenting a highly accessible introduction to this most topical area, this title provides a comprehensive understanding of fuzzy sets and their applications. A range of carefully selected topics, from fuzzy arithmetic and fuzzy programming through to qualitative and quantitative fuzzy data analysis, are discussed in detail, giving a strong framework for addressing the various applications of fuzzy sets. Features include clear explanation of the mathematical basis of fuzzy set theory, comprehensive coverage of principles and their applications, and presentation of a wide range of practical applications The growing applications of fuzzy theory ensures this book will appeal to both communication and control engineering professionals with a general background in mathematics. Computer scientists and researchers, as well as applied mathematicians, will find this an invaluable reference source providing information on current research topics Ensembles flous ram Fuzzy logic gtt Fuzzy sets gtt Fuzzy theorie gtt Logique floue ram Fuzzy sets Mathematical statistics Fuzzy logic Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Fuzzy-Menge (DE-588)4061868-7 s DE-604 Gottwald, Siegfried 1943-2015 Verfasser (DE-588)117710652 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006978416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bandemer, Hans 1932-2009 Gottwald, Siegfried 1943-2015 Fuzzy sets, fuzzy logic, fuzzy methods with applications Ensembles flous ram Fuzzy logic gtt Fuzzy sets gtt Fuzzy theorie gtt Logique floue ram Fuzzy sets Mathematical statistics Fuzzy logic Fuzzy-Menge (DE-588)4061868-7 gnd |
| subject_GND | (DE-588)4061868-7 |
| title | Fuzzy sets, fuzzy logic, fuzzy methods with applications |
| title_auth | Fuzzy sets, fuzzy logic, fuzzy methods with applications |
| title_exact_search | Fuzzy sets, fuzzy logic, fuzzy methods with applications |
| title_full | Fuzzy sets, fuzzy logic, fuzzy methods with applications Hans Bandemer ; Siegfried Gottwald |
| title_fullStr | Fuzzy sets, fuzzy logic, fuzzy methods with applications Hans Bandemer ; Siegfried Gottwald |
| title_full_unstemmed | Fuzzy sets, fuzzy logic, fuzzy methods with applications Hans Bandemer ; Siegfried Gottwald |
| title_short | Fuzzy sets, fuzzy logic, fuzzy methods |
| title_sort | fuzzy sets fuzzy logic fuzzy methods with applications |
| title_sub | with applications |
| topic | Ensembles flous ram Fuzzy logic gtt Fuzzy sets gtt Fuzzy theorie gtt Logique floue ram Fuzzy sets Mathematical statistics Fuzzy logic Fuzzy-Menge (DE-588)4061868-7 gnd |
| topic_facet | Ensembles flous Fuzzy logic Fuzzy sets Fuzzy theorie Logique floue Mathematical statistics Fuzzy-Menge |
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