Mathematics Of Fuzzy Sets


Mathematics Of Fuzzy Sets
Author: Ulrich Höhle
Publisher: Springer Science & Business Media
ISBN: 9780792383888
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Mathematics Of Fuzzy Sets

eBook File: Mathematics-of-fuzzy-sets.PDF Book by Ulrich Höhle, Mathematics Of Fuzzy Sets Books available in PDF, EPUB, Mobi Format. Download Mathematics Of Fuzzy Sets books, 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–Jacobi equation and optimization problems. Chapter 14 surveys briefly the fundamentals of fuzzy random variables which are [0,1]-valued interpretations of random sets.


INTRODUCTION TO FUZZY SETS AND FUZZY LOGIC
Language: en
Pages: 256
Authors: M. GANESH
Categories: Mathematics
Type: BOOK - Published: 2006-01-01 - Publisher: PHI Learning Pvt. Ltd.
Reflecting the tremendous advances that have taken place in the study of fuzzy set theory and fuzzy logic, this book not only details the theoretical advances in these areas, but also considers a broad variety of applications of fuzzy sets and fuzzy logic. This comprehensive and up-to-date text is organized
Mathematics of Fuzzy Sets
Language: en
Pages: 716
Authors: Ulrich Höhle, S.E. Rodabaugh
Categories: Business & Economics
Type: BOOK - Published: 1999 - Publisher: Springer Science & Business Media
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
Mathematics of Fuzzy Sets and Fuzzy Logic
Language: en
Pages: 276
Authors: Barnabas Bede
Categories: Computers
Type: BOOK - Published: 2012-12-14 - Publisher: Springer
This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for mathematician, scientists or engineers who would like to get an insight into Fuzzy Logic. Fuzzy Sets
Fuzzy Sets Theory and Applications
Language: en
Pages: 403
Authors: André Jones, Arnold Kaufmann, Hans-Jürgen Zimmermann
Categories: Mathematics
Type: BOOK - Published: 1986-06-30 - Publisher: Springer Science & Business Media
Problems in decision making and in other areas such as pattern recogni tion, control, structural engineering etc. involve numerous aspects of uncertainty. Additional vagueness is introduced as models become more complex but not necessarily more meaningful by the added details. During the last two decades one has become more and
Fundamentals of Fuzzy Sets
Language: en
Pages: 647
Authors: Didier Dubois, Henri Prade, Henri M. Prade
Categories: Business & Economics
Type: BOOK - Published: 2000 - Publisher: Springer Science & Business Media
Fundamentals of Fuzzy Sets covers the basic elements of fuzzy set theory. Its four-part organization provides easy referencing of recent as well as older results in the field. The first part discusses the historical emergence of fuzzy sets, and delves into fuzzy set connectives, and the representation and measurement of
Fuzzy Logic with Engineering Applications
Language: en
Pages: 628
Authors: Timothy J. Ross
Categories: Technology & Engineering
Type: BOOK - Published: 2004-08-16 - Publisher: John Wiley & Sons
Fuzzy logic refers to a set of methods used to characterize and quantify uncertainty in engineering systems. This edition covers major advances that have been made with regard to both theory and applications.
Mathematics of Fuzziness—Basic Issues
Language: en
Pages: 220
Authors: Xuzhu Wang, Da Ruan, Etienne E. Kerre
Categories: Mathematics
Type: BOOK - Published: 2009-04-03 - Publisher: Springer Science & Business Media
Mathematics of Fuzziness – Basic Issues introduces a basic notion of ‘fuzziness’ and provides a conceptual mathematical framework to characterize such fuzzy phenomena in Studies in Fuzziness and Soft Computing. The book systematically presents a self-contained introduction to the essentials of mathematics of fuzziness ranging from fuzzy sets, fuzzy relations,
The Journal of Fuzzy Mathematics
Language: en
Pages:
Authors: Xuzhu Wang, Da Ruan, Etienne E. Kerre
Categories: Fuzzy arithmetic
Type: BOOK - Published: 2008 - Publisher:
Books about The Journal of Fuzzy Mathematics
Fuzzy Set Theory—and Its Applications
Language: en
Pages: 514
Authors: Hans-Jürgen Zimmermann
Categories: Business & Economics
Type: BOOK - Published: 2001-11-30 - Publisher: Springer Science & Business Media
This introduction to fuzzy set theory and its multitude of applications seeks to balance the character of the book with the dynamic nature of the research. This edition includes new chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy
Fuzzy Mathematics
Language: en
Pages: 286
Authors: Etienne E. Kerre, John Mordeson
Categories: Business & Economics
Type: BOOK - Published: 2018-11-28 - Publisher: MDPI
This book is a printed edition of the Special Issue "Fuzzy Mathematics" that was published in Mathematics