Fuzzy sets and their applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Bristol u.a.
Hilger
1989
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 248 S. graph. Darst. |
| ISBN: | 0852745834 |
Staff View
MARC
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Record in the Search Index
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| adam_text | CONTENTS
INTRODUCTION 11
PART I Theory 13
1. SURVEY OF THE FUNDAMENTAL NOTIONS . 14
1.1 Sets and basic operations 14
1.1.1 Classes and sets 14
1.1.2 Basic operations 15
1.2 Relations and structures 16
1.2.1 Relations and functions 16
1.2.2 Structures 18
1.3 First order logic 22
1.4 Formal languages 24
2. FUZZY SET THEORY 27
2.1 Reasoning on the notion of a fuzzy set 27
2.2 The notion of a fuzzy set 29
2.2.1 Definition of a fuzzy set 29
2.2.2 The lattice of membership grades 32
2.2.3 Representation theorem and cardinality of
fuzzy sets 43
2.3 Operations on fuzzy sets 46
2.3.1 Basic operations 46
2.3.2 Other important notions and their properties . 51
2.3.3 Extension principle 57
2.3.4 Operations on fuzzy sets of type 2 .... 60
2.3.5 Measures of fuzziness 62
2.4 Fuzzy structures 66
2.4.1 Fuzzy relations and structures 67
2.4.l(a) Fuzzy relations and functions 67
2.4. l(b) Fuzzy relation equations 74
2.4.l(c) Fuzzy functions 78
2.4.2 Similarity relations 82
2.4.3 Special fuzzy structures 85
7
2.4.3(a) Fuzzy ordering 86
2.4.3(b) Fuzzy groups 87
2.4.3(c) Fuzzy topology 88
2.4.3(d) Probability of fuzzy events 89
2.5 Fuzzy numbers 91
2.5.1 Basic properties of fuzzy numbers .... 91
2.5.2 Basic operations on fuzzy numbers .... 95
2.5.3 Ordering of fuzzy numbers 98
3. THE MODEL OF NATURAL LANGUAGE
SEMANTICS AND LINGUISTIC VARIABLES . . 101
3.1 The model of natural language semantics 101
3.1.1 The semantics of words 101
3.1.2 The semantics of expressions 104
3.1.3 Linguistic modifiers 110
3.2 Linguistic variables 117
3.3 The linguistic approximation 120
4. FUZZY LOGIC 127
4.1 Many valued first order fuzzy logic 127
4.1.1 Introduction 127
4.1.2 Truth values and generalised functions . . . 128
4.1.3 Syntax and semantics of first order fuzzy
logic 130
4.1.4 Fuzzy theories of the first order 138
4.1.5 Completeness theorems 142
4.2 Linguistic logic 144
4.2.1 Linguistic truth values 145
4.2.2 Expressing linguistic truth values 147
4.3 Approximate reasoning 148
PART II Applications 153
5. DECISION AND CONTROL 154
5.1 Decision 154
5.1.1 Decision in a fuzzy environment 154
5.1.2 Determination of weights 158
5.1.3 Decision based on aggregation of preferences 161
5.1.4 Decision based on a linguistically expressed
contribution of alternatives 162
5.2 Control 166
5.2.1 The fuzzy controller 166
8
5.2.2 Examples of fuzzy controllers 171
5.3 Presentation of information 174
5.3.1 Reduction of information 174
5.3.2 Toleration search of misspelled words . . . 174
6. FUZZY SYSTEMS 181
6.1 Dynamic fuzzy systems 181
6.2 General fuzzy models, examples and methodology . 186
6.2.1 General fuzzy models 186
6.2.2 Some examples of fuzzy models 189
6.2.3 Methodology of fuzzy model construction . 192
6.3 Evaluation of system behaviour 193
6.4 Preference of system parameters 196
6.5 Fuzzy automata 201
7. FUZZY ALGORITHMS AND PROGRAMMING
LANGUAGES 205
7.1 Fuzzy algorithms 205
7.1.1 The concept of the fuzzy algorithm .... 207
7.1.2 Interpretation and execution of fuzzy
instructions 211
7.2 Linguistically oriented programming languages . . . 211
7.2.1 Introduction 211
7.2.2 The programming language L.P.L 211
7.2.3 The possible applications of linguistically
oriented programming languages 214
8. OTHER APPLICATIONS 216
8.1 Linear programming 216
8.2 Cluster analysis and pattern recognition 217
8.3 Situation analysis in power system working . . . . 218
8.4 Database systems 219
8.5 Psychology 220
8.6 Applications in other fields 221
9. GENERAL PROBLEMS OF FUZZY SET THEORY 222
9.1 Determination of the membership function .... 222
9.2 Theoretical problems with the foundations of fuzzy
set theory 226
9.2.1 Vagueness and indiscernibility 226
9.2.2 Alternative set theory 227
9.2.3 Fuzzy equality and nebulae 229
9
9.2.4 Axiomatisation of fuzzy sets 231
9.2.5 Discussion 232
9.3 Historical remarks 233
A short dictionary of fundamental terms 235
REFERENCES 236
INDEX 245
10
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| discipline | Informatik Mathematik |
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| id | DE-604.BV003712981 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:04:15Z |
| institution | BVB |
| isbn | 0852745834 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002363332 |
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| physical | 248 S. graph. Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Hilger |
| record_format | marc |
| spelling | Novák, Vilém 1951- Verfasser (DE-588)122261666 aut Fuzzy sets and their applications Bristol u.a. Hilger 1989 248 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fuzzy sets Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Fuzzy-Menge (DE-588)4061868-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002363332&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Novák, Vilém 1951- Fuzzy sets and their applications Fuzzy sets Fuzzy-Menge (DE-588)4061868-7 gnd |
| subject_GND | (DE-588)4061868-7 |
| title | Fuzzy sets and their applications |
| title_auth | Fuzzy sets and their applications |
| title_exact_search | Fuzzy sets and their applications |
| title_full | Fuzzy sets and their applications |
| title_fullStr | Fuzzy sets and their applications |
| title_full_unstemmed | Fuzzy sets and their applications |
| title_short | Fuzzy sets and their applications |
| title_sort | fuzzy sets and their applications |
| topic | Fuzzy sets Fuzzy-Menge (DE-588)4061868-7 gnd |
| topic_facet | Fuzzy sets Fuzzy-Menge |
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