Fuzzy logic and mathematics : a historical perspective
The term “fuzzy logic” (FL) is a generic one, which stands for a broad variety of logical systems. Their common ground is the rejection of the most fundamental principle of classical logic—the principle of bivalence—according to which each declarative sentence has exactly two possible truth values—t...
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| Hlavní autori: | , , |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | English |
| Vydavateľské údaje: |
New York
Oxford University Press
2017
Oxford University Press, Incorporated |
| Vydanie: | 1 |
| Predmet: | |
| ISBN: | 0190200014, 9780190200015 |
| On-line prístup: | Získať plný text |
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- Cover -- Half title -- Title -- Copyright -- Contents -- Preface -- Notes for the Reader -- Chapter 1 Aims and Scope of This Book -- Chapter 2 Prehistory, Emergence, and Evolution of Fuzzy Logic -- 2.1 Prehistory of fuzzy logic -- 2.2 Emergence of fuzzy logic -- 2.3 Evolving attitudes toward fuzzy logic -- 2.4 Documented debates -- 2.5 Evolution of supporting infrastructure for fuzzy logic -- Chapter 3 Fuzzy Logic in the Broad Sense -- 3.1 Introduction -- 3.2 Basic concepts of fuzzy sets -- 3.3 Operations on fuzzy sets -- 3.4 Fuzzy intervals, fuzzy numbers, and fuzzy arithmetic -- 3.5 Fuzzy relations -- 3.6 Approximate reasoning -- 3.7 Possibility theory -- 3.8 Fuzzy clustering -- 3.9 Methods for constructing fuzzy sets -- 3.10 Nonstandard fuzzy sets -- Chapter 4 Fuzzy Logic in the Narrow Sense -- 4.1 From classical to fuzzy logic: Principal issues -- 4.2 Many-valued logics until the 1960s -- 4.2.1 Łukasiewicz finitely- and infinitely-valued logics -- 4.2.2 Gödel finitely- and infinitely-valued logics -- 4.2.3 Other propositional logics -- 4.2.4 Predicate logics -- 4.2.5 Further developments -- 4.2.6 The mid-1960s and Zadeh's idea of fuzzy sets -- 4.3 Fuzzy logics with graded consequence -- 4.3.1 Goguen's logic of inexact concepts -- 4.3.2 Pavelka-style fuzzy logic -- 4.3.3 Further developments -- 4.4 Fuzzy logics based on t-norms and their residua -- 4.4.1 Fuzzy logics based on t-norms until the mid-1990s -- 4.4.2 Product logic -- 4.4.3 Hájek's logic BL and Metamathematics of Fuzzy Logic -- 4.4.4 Logics related to BL -- 4.5 Fuzzy logic and uncertainty -- 4.5.1 Degrees of truth vs. belief and truth functionality -- 4.5.2 Possibilistic logic -- 4.5.3 Gerla's probabilistic fuzzy logics -- 4.5.4 Belief, modality, and quantifiers in fuzzy logic -- 4.6 Miscellaneous issues -- 4.6.1 Relationship to applications -- 4.6.2 Computability and complexity
- Subject Index
- 4.6.3 Further developments -- Chapter 5 Mathematics Based on Fuzzy Logic -- 5.1 Principal issues and outline of development -- 5.1.1 What is mathematics based on fuzzy logic? -- 5.1.2 The problem and role of foundations -- 5.1.3 The problem and role of applications -- 5.1.4 Outline of development -- 5.2 Foundations of mathematics based on fuzzy logic -- 5.2.1 The role of fuzzy logic in the narrow sense -- 5.2.2 Higher-order logic approaches -- 5.2.3 Set-theoretic approaches -- 5.2.4 Category-theoretic approaches -- 5.3 Selected areas of mathematics based on fuzzy logic -- 5.3.1 Sets and relations -- 5.3.2 Algebra -- 5.3.3 Topology -- 5.3.4 Quantities and mathematical analysis -- 5.3.5 Probability and statistics -- 5.3.6 Geometry -- 5.3.7 Further developments -- 5.4 Miscellaneous issues -- 5.4.1 Interpretation of truth degrees -- 5.4.2 Fuzzy logic and paradoxes -- 5.4.3 Fuzzy logic and vagueness -- Chapter 6 Applications of Fuzzy Logic -- 6.1 Introduction -- 6.2 A historical overview -- 6.3 Engineering -- 6.3.1 Fuzzy control -- 6.3.2 Other engineering applications -- 6.4 Decision making -- 6.5 Natural sciences -- 6.5.1 Chemistry -- 6.5.2 Biology -- 6.5.3 Physics -- 6.6 Earth sciences -- 6.7 Psychology -- 6.8 Social sciences -- 6.8.1 A historical overview -- 6.8.2 Economics -- 6.8.3 Political science -- 6.9 Computer science -- 6.10 Medicine -- 6.11 Management and business -- 6.12 Other applications -- Chapter 7 Significance of Fuzzy Logic -- 7.1 Introduction -- 7.2 A retrospective overview of fuzzy logic -- 7.3 Paradigm shifts in science, mathematics, engineering, and other areas -- 7.4 Assessment of the significance of fuzzy logic -- 7.5 A prospective view on the 50th anniversary of fuzzy logic -- Appendix A The Enigma of Cox's Proof -- Appendix B Overview of Classical Logic -- Appendix C Photographs -- Glossary of Symbols -- References -- Name Index