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Books > Science & Mathematics > Mathematics > Applied mathematics > Fuzzy set theory
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Mathematics of Fuzzy Sets - Logic, Topology, and Measure Theory (Hardcover, 1999 ed.)
Loot Price: R8,028
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Mathematics of Fuzzy Sets - Logic, Topology, and Measure Theory (Hardcover, 1999 ed.)
Series: The Handbooks of Fuzzy Sets, 3
Expected to ship within 18 - 22 working days
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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 orcomplete [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.
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