Fundamentals Of Fuzzy Sets

Author : Didier Dubois,Henri Prade
Publisher : Springer Science & Business Media
Page : 660 pages
File Size : 49,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461544296

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Fundamentals of Fuzzy Sets by Didier Dubois,Henri Prade Pdf

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 membership functions. The second part covers fuzzy relations, including orderings, similarity, and relational equations. The third part, devoted to uncertainty modelling, introduces possibility theory, contrasting and relating it with probabilities, and reviews information measures of specificity and fuzziness. The last part concerns fuzzy sets on the real line - computation with fuzzy intervals, metric topology of fuzzy numbers, and the calculus of fuzzy-valued functions. Each chapter is written by one or more recognized specialists and offers a tutorial introduction to the topics, together with an extensive bibliography.

Author : James J. Buckley,Esfandiar Eslami
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 44,7 Mb
Release : 2013-11-11
Category : Computers
ISBN : 9783790817997

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An Introduction to Fuzzy Logic and Fuzzy Sets by James J. Buckley,Esfandiar Eslami Pdf

This book is an excellent starting point for any curriculum in fuzzy systems fields such as computer science, mathematics, business/economics and engineering. It covers the basics leading to: fuzzy clustering, fuzzy pattern recognition, fuzzy database, fuzzy image processing, soft computing, fuzzy applications in operations research, fuzzy decision making, fuzzy rule based systems, fuzzy systems modeling, fuzzy mathematics. It is not a book designed for researchers - it is where you really learn the "basics" needed for any of the above-mentioned applications. It includes many figures and problem sets at the end of sections.

Author : Witold Pedrycz
Publisher : Springer Nature
Page : 287 pages
File Size : 54,9 Mb
Release : 2020-08-11
Category : Technology & Engineering
ISBN : 9783030528003

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An Introduction to Computing with Fuzzy Sets by Witold Pedrycz Pdf

This book provides concise yet thorough coverage of the fundamentals and technology of fuzzy sets. Readers will find a lucid and systematic introduction to the essential concepts of fuzzy set-based information granules, their processing and detailed algorithms. Timely topics and recent advances in fuzzy modeling and its principles, neurocomputing, fuzzy set estimation, granulation–degranulation, and fuzzy sets of higher type and order are discussed. In turn, a wealth of examples, case studies, problems and motivating arguments, spread throughout the text and linked with various areas of artificial intelligence, will help readers acquire a solid working knowledge. Given the book’s well-balanced combination of the theory and applied facets of fuzzy sets, it will appeal to a broad readership in both academe and industry. It is also ideally suited as a textbook for graduate and undergraduate students in science, engineering, and operations research.

Author : George J. Klir,Ute H. St. Clair,Bo Yuan
Publisher : Unknown
Page : 264 pages
File Size : 40,7 Mb
Release : 1997
Category : Computers
ISBN : UOM:39015041012140

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Fuzzy Set Theory by George J. Klir,Ute H. St. Clair,Bo Yuan Pdf

Fuzzy Set Theory: Foundations and Applications serves as a simple introduction to basic elements of fuzzy set theory. The emphasis is on a conceptual rather than a theoretical presentation of the material. Fuzzy Set Theory also contains an overview of the corresponding elements of classical set theory - including basic ideas of classical relations - as well as an overview of classical logic. Because the inclusion of background material in these classical foundations provides a self-contained course of study, students from many different academic backgrounds will have access to this important new theory.

Author : Rafik Aziz Aliev
Publisher : Springer
Page : 324 pages
File Size : 44,8 Mb
Release : 2013-01-12
Category : Technology & Engineering
ISBN : 9783642348952

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Fundamentals of the Fuzzy Logic-Based Generalized Theory of Decisions by Rafik Aziz Aliev Pdf

Every day decision making and decision making in complex human-centric systems are characterized by imperfect decision-relevant information. Main drawback of the existing decision theories is namely incapability to deal with imperfect information and modeling vague preferences. Actually, a paradigm of non-numerical probabilities in decision making has a long history and arose also in Keynes’s analysis of uncertainty. There is a need for further generalization – a move to decision theories with perception-based imperfect information described in NL. The languages of new decision models for human-centric systems should be not languages based on binary logic but human-centric computational schemes able to operate on NL-described information. Development of new theories is now possible due to an increased computational power of information processing systems which allows for computations with imperfect information, particularly, imprecise and partially true information, which are much more complex than computations over numbers and probabilities. The monograph exposes the foundations of a new decision theory with imperfect decision-relevant information on environment and a decision maker’s behavior. This theory is based on the synthesis of the fuzzy sets theory with perception-based information and the probability theory. The book is self containing and represents in a systematic way the decision theory with imperfect information into the educational systems. The book will be helpful for teachers and students of universities and colleges, for managers and specialists from various fields of business and economics, production and social sphere.

Author : Ying Bai,Hanqi Zhuang,Dali Wang
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 46,8 Mb
Release : 2007-01-17
Category : Technology & Engineering
ISBN : 9781846284694

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Advanced Fuzzy Logic Technologies in Industrial Applications by Ying Bai,Hanqi Zhuang,Dali Wang Pdf

This book introduces a dynamic, on-line fuzzy inference system. In this system membership functions and control rules are not determined until the system is applied and each output of its lookup table is calculated based on current inputs. The book describes the real-world uses of new fuzzy techniques to simplify readers’ tuning processes and enhance the performance of their control systems. It further contains application examples.

Author : Ulrich Höhle,S.E. Rodabaugh
Publisher : Springer Science & Business Media
Page : 732 pages
File Size : 47,7 Mb
Release : 1998-12-31
Category : Business & Economics
ISBN : 0792383885

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Mathematics of Fuzzy Sets by Ulrich Höhle,S.E. Rodabaugh Pdf

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.

Author : Hans Bandemer,Siegfried Gottwald
Publisher : Unknown
Page : 264 pages
File Size : 55,9 Mb
Release : 1995
Category : Computers
ISBN : UOM:39015034286024

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Fuzzy Sets, Fuzzy Logic, Fuzzy Methods with Applications by Hans Bandemer,Siegfried Gottwald Pdf

This highly accessible introduction to the fundamentals of fuzzy sets and their applications covers fuzzy numbers, fuzzy programming, fuzzy controllers, qualitative fuzzy data analysis, and much more.

Author : Umberto Straccia
Publisher : CRC Press
Page : 388 pages
File Size : 49,7 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781000556780

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Foundations of Fuzzy Logic and Semantic Web Languages (Open Access) by Umberto Straccia Pdf

Managing vagueness/fuzziness is starting to play an important role in Semantic Web research, with a large number of research efforts underway. Foundations of Fuzzy Logic and Semantic Web Languages provides a rigorous and succinct account of the mathematical methods and tools used for representing and reasoning with fuzzy information within Semantic

Author : George J. Klir
Publisher : Diderot Editeur Arts Sciences
Page : 203 pages
File Size : 43,5 Mb
Release : 1996
Category : Логика
ISBN : 2841340120

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Fuzzy Sets by George J. Klir Pdf

Author : Tamalika Chaira
Publisher : John Wiley & Sons
Page : 304 pages
File Size : 44,9 Mb
Release : 2019-03-21
Category : Technology & Engineering
ISBN : 9781119544210

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Fuzzy Set and Its Extension by Tamalika Chaira Pdf

Provides detailed mathematical exposition of the fundamentals of fuzzy set theory, including intuitionistic fuzzy sets This book examines fuzzy and intuitionistic fuzzy mathematics and unifies the latest existing works in literature. It enables readers to fully understand the mathematics of both fuzzy set and intuitionistic fuzzy set so that they can use either one in their applications. Each chapter of Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set begins with an introduction, theory, and several examples to guide readers along. The first one starts by laying the groundwork of fuzzy/intuitionistic fuzzy sets, fuzzy hedges, and fuzzy relations. The next covers fuzzy numbers and explains Zadeh's extension principle. Then comes chapters looking at fuzzy operators; fuzzy similarity measures and measures of fuzziness; and fuzzy/intuitionistic fuzzy measures and fuzzy integrals. The book also: discusses the definition and properties of fuzzy measures; examines matrices and determinants of a fuzzy matrix; and teaches about fuzzy linear equations. Readers will also learn about fuzzy subgroups. The second to last chapter examines the application of fuzzy and intuitionistic fuzzy mathematics in image enhancement, segmentation, and retrieval. Finally, the book concludes with coverage the extension of fuzzy sets. This book: Covers both fuzzy and intuitionistic fuzzy sets and includes examples and practical applications Discusses intuitionistic fuzzy integrals and recent aggregation operators using Choquet integral, with examples Includes a chapter on applications in image processing using fuzzy and intuitionistic fuzzy sets Explains fuzzy matrix operations and features examples Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set is an ideal text for graduate and research students, as well as professionals, in image processing, decision-making, pattern recognition, and control system design.

Author : George J. Klir,Bo Yuan
Publisher : Prentice Hall
Page : 600 pages
File Size : 47,5 Mb
Release : 1995
Category : Computers
ISBN : UOM:39015034424906

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Fuzzy Sets and Fuzzy Logic by George J. Klir,Bo Yuan Pdf

No previous knowledge of fuzzy set theory and fuzzy logic is required for understanding the material covered in the book. Although knowledge of basic ideas of classical (nonfuzzy) set theory and classical (two-valued) logic is useful, fundamentals of these subject areas are briefly overviewed in the book. In addition, basic ideas of neural networks, genetic algorithms, and rough sets are also explained. This makes the book virtually self-contained.

Author : James M. Keller,Derong Liu,David B. Fogel
Publisher : John Wiley & Sons
Page : 378 pages
File Size : 50,7 Mb
Release : 2016-07-13
Category : Technology & Engineering
ISBN : 9781119214366

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Fundamentals of Computational Intelligence by James M. Keller,Derong Liu,David B. Fogel Pdf

Provides an in-depth and even treatment of the three pillars of computational intelligence and how they relate to one another This book covers the three fundamental topics that form the basis of computational intelligence: neural networks, fuzzy systems, and evolutionary computation. The text focuses on inspiration, design, theory, and practical aspects of implementing procedures to solve real-world problems. While other books in the three fields that comprise computational intelligence are written by specialists in one discipline, this book is co-written by current former Editor-in-Chief of IEEE Transactions on Neural Networks and Learning Systems, a former Editor-in-Chief of IEEE Transactions on Fuzzy Systems, and the founding Editor-in-Chief of IEEE Transactions on Evolutionary Computation. The coverage across the three topics is both uniform and consistent in style and notation. Discusses single-layer and multilayer neural networks, radial-basis function networks, and recurrent neural networks Covers fuzzy set theory, fuzzy relations, fuzzy logic interference, fuzzy clustering and classification, fuzzy measures and fuzzy integrals Examines evolutionary optimization, evolutionary learning and problem solving, and collective intelligence Includes end-of-chapter practice problems that will help readers apply methods and techniques to real-world problems Fundamentals of Computational intelligence is written for advanced undergraduates, graduate students, and practitioners in electrical and computer engineering, computer science, and other engineering disciplines.

Author : Phil Diamond,Peter E. Kloeden
Publisher : World Scientific
Page : 192 pages
File Size : 40,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9810217315

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Metric Spaces of Fuzzy Sets by Phil Diamond,Peter E. Kloeden Pdf

The primary aim of the book is to provide a systematic development of the theory of metric spaces of normal, upper semicontinuous fuzzy convex fuzzy sets with compact support sets, mainly on the base space ?n. An additional aim is to sketch selected applications in which these metric space results and methods are essential for a thorough mathematical analysis.This book is distinctly mathematical in its orientation and style, in contrast with many of the other books now available on fuzzy sets, which, although all making use of mathematical formalism to some extent, are essentially motivated by and oriented towards more immediate applications and related practical issues. The reader is assumed to have some previous undergraduate level acquaintance with metric spaces and elementary functional analysis.

Author : Patricia Melin,Oscar Castillo,Luis T. Aguilar,Witold Pedrycz
Publisher : Springer Science & Business Media
Page : 832 pages
File Size : 46,8 Mb
Release : 2007-07-02
Category : Computers
ISBN : 9783540729501

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Foundations of Fuzzy Logic and Soft Computing by Patricia Melin,Oscar Castillo,Luis T. Aguilar,Witold Pedrycz Pdf

This book comprises a selection of papers from IFSA 2007 on new methods and theories that contribute to the foundations of fuzzy logic and soft computing. Coverage includes the application of fuzzy logic and soft computing in flexible querying, philosophical and human-scientific aspects of soft computing, search engine and information processing and retrieval, as well as intelligent agents and knowledge ant colony.