Fundamentals Of Fuzzy Sets

Author : Didier Dubois
Publisher : Springer Science & Business Media
ISBN 13 : 1461544297
Total Pages : 660 pages
Book Rating : 4.96/5 ( download)

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Download or read book Fundamentals of Fuzzy Sets written by Didier Dubois and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Rafik Aziz Aliev
Publisher : Springer
ISBN 13 : 3642348955
Total Pages : 332 pages
Book Rating : 4.52/5 ( download)

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Download or read book Fundamentals of the Fuzzy Logic-Based Generalized Theory of Decisions written by Rafik Aziz Aliev and published by Springer. This book was released on 2013-01-12 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Witold Pedrycz
Publisher : Springer Nature
ISBN 13 : 3030528006
Total Pages : 287 pages
Book Rating : 4.03/5 ( download)

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Download or read book An Introduction to Computing with Fuzzy Sets written by Witold Pedrycz and published by Springer Nature. This book was released on 2020-08-11 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : R. Lowen
Publisher : Springer Science & Business Media
ISBN 13 : 9401587418
Total Pages : 415 pages
Book Rating : 4.19/5 ( download)

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Download or read book Fuzzy Set Theory written by R. Lowen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide the reader who is interested in applications of fuzzy set theory, in the first place with a text to which he or she can refer for the basic theoretical ideas, concepts and techniques in this field and in the second place with a vast and up to date account of the literature. Although there are now many books about fuzzy set theory, and mainly about its applications, e. g. in control theory, there is not really a book available which introduces the elementary theory of fuzzy sets, in what I would like to call "a good degree of generality". To write a book which would treat the entire range of results concerning the basic theoretical concepts in great detail and which would also deal with all possible variants and alternatives of the theory, such as e. g. rough sets and L-fuzzy sets for arbitrary lattices L, with the possibility-probability theories and interpretations, with the foundation of fuzzy set theory via multi-valued logic or via categorical methods and so on, would have been an altogether different project. This book is far more modest in its mathematical content and in its scope.

Author : Ulrich Höhle
Publisher : Springer Science & Business Media
ISBN 13 : 1461550793
Total Pages : 722 pages
Book Rating : 4.92/5 ( download)

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Download or read book Mathematics of Fuzzy Sets written by Ulrich Höhle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.24/5 ( download)

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Download or read book Fuzzy Sets, Fuzzy Logic, Fuzzy Methods with Applications written by Hans Bandemer and published by . This book was released on 1995 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Guanrong Chen
Publisher : CRC Press
ISBN 13 : 1420039814
Total Pages : 329 pages
Book Rating : 4.18/5 ( download)

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Download or read book Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems written by Guanrong Chen and published by CRC Press. This book was released on 2000-11-27 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the early 1970s, fuzzy systems and fuzzy control theories added a new dimension to control systems engineering. From its beginnings as mostly heuristic and somewhat ad hoc, more recent and rigorous approaches to fuzzy control theory have helped make it an integral part of modern control theory and produced many exciting results. Yesterday's "art

Author : Umberto Straccia
Publisher : CRC Press
ISBN 13 : 1000556786
Total Pages : 388 pages
Book Rating : 4.80/5 ( download)

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Download or read book Foundations of Fuzzy Logic and Semantic Web Languages (Open Access) written by Umberto Straccia and published by CRC Press. This book was released on 2016-04-19 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Tamalika Chaira
Publisher : John Wiley & Sons
ISBN 13 : 1119544211
Total Pages : 304 pages
Book Rating : 4.10/5 ( download)

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Download or read book Fuzzy Set and Its Extension written by Tamalika Chaira and published by John Wiley & Sons. This book was released on 2019-03-21 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.40/5 ( download)

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Download or read book Fuzzy Set Theory written by George J. Klir and published by . This book was released on 1997 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.