Mathematics of Fuzzy Sets
Language: English
Published by Kluwer Academic Publishers, 1998
- Hardcover
- New
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Deals with non-classical logics and their semantic foundations. This work details the lattice-theoretic foundations of image powerset operators. It relates lattice-valued topologies to probabilistic topological spaces and fuzzy neighbourhood spaces. It lays the foundations of generalized measure theory and representation by Markov kernels. Series: The Handbooks of Fuzzy Sets. Num Pages: 716 pages, biography. BIC Classification: PBCH; PBWX. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 240 x 163 x 44. Weight in Grams: 1178. . 1998. Hardback. . . . . Books ship from the US and Ireland.
Seller Inventory # V9780792383888
- Title
- Mathematics of Fuzzy Sets
- Author
- Hohle, Ulrich; Rodabaugh, Stephen Ernest
- Publisher
- Kluwer Academic Publishers
- Publication year
- 1998
- Condition
- New
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 0792383885
- ISBN 13
- 9780792383888
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.
"Synopsis" may belong to another edition of this title.
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