Fuzzy logic and mathematics: a historical perspective
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Oxford University Press
[2017]
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 531 Seiten 24 cm |
| ISBN: | 9780190200015 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Titel: Fuzzy logic and mathematics
Autor: Bělohlávek, Radim
Jahr: 2017
Contents
Preface ix
Notes for the Reader xi
i Aims and Scope ofThis Book i
2, Prehistory, Emergence, and Evolution ofFuzzy Logic 5
2.1 Prehistory of fuzzy logic 5
2.2 Emergence of fuzzy logic 17
2.3 Evolving attitudes toward fuzzy logic 27
2.4 Documented debates 32
2.5 Evolution of supporting infrastructure for fuzzy logic 38
3 Fuzzy Logic in the Broad Sense 43
3.1 Introduction 43
3.2 Basic concepts of fuzzy sets 44
3.3 Operations on fuzzy sets 46
3.4 Fuzzy intervals, fuzzy numbers, and fuzzy arithmetic 55
3.5 Fuzzy relations 60
3.6 Approximate reasoning 69
3.7 Possibility theory 79
3.8 Fuzzy clustering 88
3.9 Methods for constructing fuzzy sets 94
3.10 Nonstandard fuzzy sets 99
4 Fuzzy Logic in the Narrow Sense 105
4.1 From classical to fuzzy logic: Principal issues 106
4.2 Many-valued logics until the 1960s 112
4.2.1 Lukasiewicz finitely- and infinitely-valued logics 112
4.2.2 Gödel finitely- and infinitely-valued logics 129
4.2.3 Other propositional logics 134
vi
Contents
4.2.4 Predicate logics H 7
4.2.5 Further developments 155
4.2.6 The mid-i96os and Zadeh sideaof fuzzy sets 159
4.3 Fuzzy logics with graded consequence 160
4.3.1 Goguen s logic of inexact concepts 161
4.3.2 Pavelka-style fuzzy logic 165
4.3.3 Further developments 171
4.4 Fuzzy logics based on t-norms and their residua 177
4.4.1 Fuzzy logics based on t-norms until the mid-i99os 178
4.4.2 Product logic 187
4.4.3 Hajek s logic BL and Metamathematics of Fuzzy Logic ... 189
4.4.4 Logics related to BL 202
4.5 Fuzzy logic and uncertainty 210
4.5.1 Degrees of truth vs. belief and truth functionality 210
4.5.2 Possibilistic logic 212
4.5.3 Gerla s probabilistic fuzzy logics 215
4.5.4 Belief, modality, and quantifiers in fuzzy logic 216
4.6 Miscellaneous issues 222
4.6.1 Relationship to applications 222
4.6.2 Computability and complexity 224
4.6.3 Further developments 227
5 Mathematics Based on Fuzzy Logic 231
5.1 Principal issues and outline of development 231
5.1.1 What is mathematics based on fuzzy logic? 231
5.1.2 The problem and role of foundations 233
5.1.3 The problem and role of applications 238
5.1.4 Outline of development 241
5.2 Foundations of mathematics based on fuzzy logic 246
5.2.1 The role of fuzzy logic in the narrow sense 246
5.2.2 Fligher-order logic approaches 250
5.2.3 Set-theoretic approaches 253
5.2.4 Category-theoretic approaches 261
5.3 Selected areas of mathematics based on fuzzy logic 267
5.3.1 Sets and relations 267
5.3.2 Algebra 282
5.3.3 Topology 292
5.3.4 Quantities and mathematical analysis 298
5.3.5 Probability and statistics 309
5.3.6 Geometry 315
5.3.7 Further developments 320
Contents Vli
5.4 Miscellaneous issues 321
5.4.1 Interpretation of truth degrees 321
5.4.2 Fuzzy logic and paradoxes 332
5.4.3 Fuzzy logic and vagueness 339
6 Applications of Fuzzy Logic 347
6.1 Introduction 347
6.2 A historical overview 349
6.3 Engineering 356
6.3.1 Fuzzy control 356
6.3.2 Other engineering applications 365
6.4 Decision making 371
6.5 Natural sciences 375
6.5.1 Chemistry 375
6.5.2 Biology 376
6.5.3 Physics 378
6.6 Earth sciences 382
6.7 Psychology 3^5
6.8 Social sciences 39°
6.8.1 A historical overview 39°
6.8.2 Economics 392
6.8.3 Political science 396
6.9 Computer science 399
6.10 Medicine 407
6.11 Management and business 4
6.12 Other applications 4J4
7 Significance of Fuzzy Logic 421
7.1 Introduction 421
7.2 A retrospective overview of fuzzy logic 421
7.3 Paradigm shifts in science, mathematics, engineering, and other areas 425
7.4 Assessment of the significance of fuzzy logic 43°
7.5 A prospective view on the 5oth anniversary of fuzzy logic 442
Appendices
A The Enigma of Cox s Proof 449
B Overview of Classical Logic 453
C Photographs 4 69
viii
Glossary of Symbols
References
Name Index
Subject Index
Contents
473
475
5
521
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| spelling | Bělohlávek, Radim Verfasser aut Fuzzy logic and mathematics a historical perspective Radim Bělohlávek, Joseph W. Dauben, and George J. Klir New York Oxford University Press [2017] © 2017 xii, 531 Seiten 24 cm txt rdacontent n rdamedia nc rdacarrier Geschichte gnd rswk-swf Fuzzy-Logik (DE-588)4341284-1 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Fuzzy logic Logic, Symbolic and mathematical Fuzzy-Logik (DE-588)4341284-1 s Mathematik (DE-588)4037944-9 s Geschichte z DE-604 Dauben, Joseph Warren 1944- Verfasser (DE-588)172037530 aut Klir, George J. 1932-2016 Verfasser (DE-588)174097999 aut Erscheint auch als Online-Ausgabe 978-0-19-020003-9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029818105&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bělohlávek, Radim Dauben, Joseph Warren 1944- Klir, George J. 1932-2016 Fuzzy logic and mathematics a historical perspective Fuzzy-Logik (DE-588)4341284-1 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4341284-1 (DE-588)4037944-9 |
| title | Fuzzy logic and mathematics a historical perspective |
| title_auth | Fuzzy logic and mathematics a historical perspective |
| title_exact_search | Fuzzy logic and mathematics a historical perspective |
| title_full | Fuzzy logic and mathematics a historical perspective Radim Bělohlávek, Joseph W. Dauben, and George J. Klir |
| title_fullStr | Fuzzy logic and mathematics a historical perspective Radim Bělohlávek, Joseph W. Dauben, and George J. Klir |
| title_full_unstemmed | Fuzzy logic and mathematics a historical perspective Radim Bělohlávek, Joseph W. Dauben, and George J. Klir |
| title_short | Fuzzy logic and mathematics |
| title_sort | fuzzy logic and mathematics a historical perspective |
| title_sub | a historical perspective |
| topic | Fuzzy-Logik (DE-588)4341284-1 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Fuzzy-Logik Mathematik |
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