Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1999
|
| Schriftenreihe: | The Handbooks of Fuzzy Sets Series
3 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory is a major attempt to provide much-needed coherence for the mathematics of fuzzy sets. Much of this book is new material required to standardize this mathematics, making this volume a reference tool with broad appeal as well as a platform for future research. Fourteen chapters are organized into three parts: mathematical logic and foundations (Chapters 1-2), general topology (Chapters 3-10), and measure and probability theory (Chapters 11-14). Chapter 1 deals with non-classical logics and their syntactic and semantic foundations. Chapter 2 details the lattice-theoretic foundations of image and preimage powerset operators. Chapters 3 and 4 lay down the axiomatic and categorical foundations of general topology using lattice-valued mappings as a fundamental tool. Chapter 3 focuses on the fixed-basis case, including a convergence theory demonstrating the utility of the underlying axioms. Chapter 4 focuses on the more general variable-basis case, providing a categorical unification of locales, fixed-basis topological spaces, and variable-basis compactifications. Chapter 5 relates lattice-valued topologies to probabilistic topological spaces and fuzzy neighborhood spaces. Chapter 6 investigates the important role of separation axioms in lattice-valued topology from the perspective of space embedding and mapping extension problems, while Chapter 7 examines separation axioms from the perspective of Stone-Cech-compactification and Stone-representation theorems. Chapters 8 and 9 introduce the most important concepts and properties of uniformities, including the covering and entourage approaches and the basic theory of precompact or complete [0,1]-valued uniform spaces. Chapter 10 sets out the algebraic, topological, and uniform structures of the fundamentally important fuzzy real line and fuzzy unit interval. Chapter 11 lays the foundations of generalized measure theory and representation by Markov kernels. Chapter 12 develops the important theory of conditioning operators with applications to measure-free conditioning. Chapter 13 presents elements of pseudo-analysis with applications to the Hamilton&endash;Jacobi equation and optimization problems. Chapter 14 surveys briefly the fundamentals of fuzzy random variables which are [0,1]-valued interpretations of random sets |
| Beschreibung: | 1 Online-Ressource (XII, 716 p) |
| ISBN: | 9781461550792 9781461373100 |
| ISSN: | 1388-4352 |
| DOI: | 10.1007/978-1-4615-5079-2 |
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| 500 | |a Chapter 4 focuses on the more general variable-basis case, providing a categorical unification of locales, fixed-basis topological spaces, and variable-basis compactifications. Chapter 5 relates lattice-valued topologies to probabilistic topological spaces and fuzzy neighborhood spaces. Chapter 6 investigates the important role of separation axioms in lattice-valued topology from the perspective of space embedding and mapping extension problems, while Chapter 7 examines separation axioms from the perspective of Stone-Cech-compactification and Stone-representation theorems. Chapters 8 and 9 introduce the most important concepts and properties of uniformities, including the covering and entourage approaches and the basic theory of precompact or complete [0,1]-valued uniform spaces. Chapter 10 sets out the algebraic, topological, and uniform structures of the fundamentally important fuzzy real line and fuzzy unit interval. | ||
| 500 | |a Chapter 11 lays the foundations of generalized measure theory and representation by Markov kernels. Chapter 12 develops the important theory of conditioning operators with applications to measure-free conditioning. Chapter 13 presents elements of pseudo-analysis with applications to the Hamilton&endash;Jacobi equation and optimization problems. Chapter 14 surveys briefly the fundamentals of fuzzy random variables which are [0,1]-valued interpretations of random sets | ||
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Datensatz im Suchindex
| _version_ | 1804153093377490944 |
|---|---|
| any_adam_object | |
| author | Höhle, Ulrich |
| author_facet | Höhle, Ulrich |
| author_role | aut |
| author_sort | Höhle, Ulrich |
| author_variant | u h uh |
| building | Verbundindex |
| bvnumber | BV042420899 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184365134 (DE-599)BVBBV042420899 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4615-5079-2 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461550792 9781461373100 |
| issn | 1388-4352 |
| language | English |
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| spelling | Höhle, Ulrich Verfasser aut Mathematics of Fuzzy Sets Logic, Topology, and Measure Theory edited by Ulrich Höhle, Stephen Ernest Rodabaugh Boston, MA Springer US 1999 1 Online-Ressource (XII, 716 p) txt rdacontent c rdamedia cr rdacarrier The Handbooks of Fuzzy Sets Series 3 1388-4352 Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory is a major attempt to provide much-needed coherence for the mathematics of fuzzy sets. Much of this book is new material required to standardize this mathematics, making this volume a reference tool with broad appeal as well as a platform for future research. Fourteen chapters are organized into three parts: mathematical logic and foundations (Chapters 1-2), general topology (Chapters 3-10), and measure and probability theory (Chapters 11-14). Chapter 1 deals with non-classical logics and their syntactic and semantic foundations. Chapter 2 details the lattice-theoretic foundations of image and preimage powerset operators. Chapters 3 and 4 lay down the axiomatic and categorical foundations of general topology using lattice-valued mappings as a fundamental tool. Chapter 3 focuses on the fixed-basis case, including a convergence theory demonstrating the utility of the underlying axioms. Chapter 4 focuses on the more general variable-basis case, providing a categorical unification of locales, fixed-basis topological spaces, and variable-basis compactifications. Chapter 5 relates lattice-valued topologies to probabilistic topological spaces and fuzzy neighborhood spaces. Chapter 6 investigates the important role of separation axioms in lattice-valued topology from the perspective of space embedding and mapping extension problems, while Chapter 7 examines separation axioms from the perspective of Stone-Cech-compactification and Stone-representation theorems. Chapters 8 and 9 introduce the most important concepts and properties of uniformities, including the covering and entourage approaches and the basic theory of precompact or complete [0,1]-valued uniform spaces. Chapter 10 sets out the algebraic, topological, and uniform structures of the fundamentally important fuzzy real line and fuzzy unit interval. Chapter 11 lays the foundations of generalized measure theory and representation by Markov kernels. Chapter 12 develops the important theory of conditioning operators with applications to measure-free conditioning. Chapter 13 presents elements of pseudo-analysis with applications to the Hamilton&endash;Jacobi equation and optimization problems. Chapter 14 surveys briefly the fundamentals of fuzzy random variables which are [0,1]-valued interpretations of random sets Mathematics Logic, Symbolic and mathematical Mathematical optimization Operations research Mathematical Logic and Foundations Calculus of Variations and Optimal Control; Optimization Operation Research/Decision Theory Mathematik Fuzzy-Menge (DE-588)4061868-7 gnd rswk-swf Fuzzy-Logik (DE-588)4341284-1 gnd rswk-swf Fuzzy-Logik (DE-588)4341284-1 s 1\p DE-604 Fuzzy-Menge (DE-588)4061868-7 s 2\p DE-604 Rodabaugh, Stephen Ernest Sonstige oth https://doi.org/10.1007/978-1-4615-5079-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Höhle, Ulrich Mathematics of Fuzzy Sets Logic, Topology, and Measure Theory Mathematics Logic, Symbolic and mathematical Mathematical optimization Operations research Mathematical Logic and Foundations Calculus of Variations and Optimal Control; Optimization Operation Research/Decision Theory Mathematik Fuzzy-Menge (DE-588)4061868-7 gnd Fuzzy-Logik (DE-588)4341284-1 gnd |
| subject_GND | (DE-588)4061868-7 (DE-588)4341284-1 |
| title | Mathematics of Fuzzy Sets Logic, Topology, and Measure Theory |
| title_auth | Mathematics of Fuzzy Sets Logic, Topology, and Measure Theory |
| title_exact_search | Mathematics of Fuzzy Sets Logic, Topology, and Measure Theory |
| title_full | Mathematics of Fuzzy Sets Logic, Topology, and Measure Theory edited by Ulrich Höhle, Stephen Ernest Rodabaugh |
| title_fullStr | Mathematics of Fuzzy Sets Logic, Topology, and Measure Theory edited by Ulrich Höhle, Stephen Ernest Rodabaugh |
| title_full_unstemmed | Mathematics of Fuzzy Sets Logic, Topology, and Measure Theory edited by Ulrich Höhle, Stephen Ernest Rodabaugh |
| title_short | Mathematics of Fuzzy Sets |
| title_sort | mathematics of fuzzy sets logic topology and measure theory |
| title_sub | Logic, Topology, and Measure Theory |
| topic | Mathematics Logic, Symbolic and mathematical Mathematical optimization Operations research Mathematical Logic and Foundations Calculus of Variations and Optimal Control; Optimization Operation Research/Decision Theory Mathematik Fuzzy-Menge (DE-588)4061868-7 gnd Fuzzy-Logik (DE-588)4341284-1 gnd |
| topic_facet | Mathematics Logic, Symbolic and mathematical Mathematical optimization Operations research Mathematical Logic and Foundations Calculus of Variations and Optimal Control; Optimization Operation Research/Decision Theory Mathematik Fuzzy-Menge Fuzzy-Logik |
| url | https://doi.org/10.1007/978-1-4615-5079-2 |
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