{"product_id":"9781461373100","title":"The Handbooks of Fuzzy Sets: Logic, Topology, and Measure Theory","description":"\u003ch1\u003eThe Handbooks of Fuzzy Sets: Logic, Topology, and Measure Theory\u003c\/h1\u003e \u003ch2\u003eHöhle, Ulrich; Rodabaugh, S.E.\u003c\/h2\u003e \u003cp\u003e\u003cem\u003eMathematics of Fuzzy Sets: Logic, Topology and Measure  Theory\u003c\/em\u003e 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). \u003cbr\u003e  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. \u003cbr\u003e  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. \u003cbr\u003e  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\u0026amp;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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2012-11-05\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9781461373100\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4615-5079-2\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 716\u003c\/p\u003e ","brand":"Springer US","offers":[{"title":"Default Title","offer_id":44359154172044,"sku":"9781461373100","price":341.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781461373100.jpg?v=1775733570","url":"https:\/\/lateknightbooks.com\/products\/9781461373100","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}