Mathematics Of Fuzzy Sets

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Mathematics of Fuzzy Sets and Fuzzy Logic

Barnabas Bede
Mathematics of Fuzzy Sets and Fuzzy Logic Book PDF

Author : Barnabas Bede
Publisher : Springer
Page : 281 pages
File Size : 42,5 Mb
Release : 2012-12-14
Category : Technology & Engineering
ISBN : 9783642352218

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Mathematics of Fuzzy Sets and Fuzzy Logic by Barnabas Bede Pdf

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 have been introduced by Lotfi Zadeh in 1965 and since then, they have been used in many applications. As a consequence, there is a vast literature on the practical applications of fuzzy sets, while theory has a more modest coverage. The main purpose of the present book is to reduce this gap by providing a theoretical introduction into Fuzzy Sets based on Mathematical Analysis and Approximation Theory. Well-known applications, as for example fuzzy control, are also discussed in this book and placed on new ground, a theoretical foundation. Moreover, a few advanced chapters and several new results are included. These comprise, among others, a new systematic and constructive approach for fuzzy inference systems of Mamdani and Takagi-Sugeno types, that investigates their approximation capability by providing new error estimates.

Mathematics of Fuzzy Sets

Ulrich Höhle,S.E. Rodabaugh
Mathematics of Fuzzy Sets Book PDF

Author : Ulrich Höhle,S.E. Rodabaugh
Publisher : Springer Science & Business Media
Page : 722 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461550792

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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.

Fuzzy Logic and Mathematics

Radim Bělohlávek,Joseph W. Dauben,George J. Klir
Fuzzy Logic and Mathematics Book PDF

Author : Radim Bělohlávek,Joseph W. Dauben,George J. Klir
Publisher : Oxford University Press
Page : 545 pages
File Size : 46,5 Mb
Release : 2017
Category : Mathematics
ISBN : 9780190200015

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Fuzzy Logic and Mathematics by Radim Bělohlávek,Joseph W. Dauben,George J. Klir Pdf

The main part of the book is a comprehensive overview of the development of fuzzy logic and its applications in various areas of human affair since its genesis in the mid 1960s. This overview is then employed for assessing the significance of fuzzy logic and mathematics based on fuzzy logic.

Fuzzy Mathematics

Etienne E. Kerre,John Mordeson
Fuzzy Mathematics Book PDF

Author : Etienne E. Kerre,John Mordeson
Publisher : MDPI
Page : 287 pages
File Size : 45,5 Mb
Release : 2018-11-28
Category : Electronic books
ISBN : 9783038973225

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Fuzzy Mathematics by Etienne E. Kerre,John Mordeson Pdf

This book is a printed edition of the Special Issue "Fuzzy Mathematics" that was published in Mathematics

A Modern Introduction to Fuzzy Mathematics

Apostolos Syropoulos,Theophanes Grammenos
A Modern Introduction to Fuzzy Mathematics Book PDF

Author : Apostolos Syropoulos,Theophanes Grammenos
Publisher : John Wiley & Sons
Page : 382 pages
File Size : 53,6 Mb
Release : 2020-07-28
Category : Technology & Engineering
ISBN : 9781119445289

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A Modern Introduction to Fuzzy Mathematics by Apostolos Syropoulos,Theophanes Grammenos Pdf

Provides readers with the foundations of fuzzy mathematics as well as more advanced topics A Modern Introduction to Fuzzy Mathematics provides a concise presentation of fuzzy mathematics., moving from proofs of important results to more advanced topics, like fuzzy algebras, fuzzy graph theory, and fuzzy topologies. The authors take the reader through the development of the field of fuzzy mathematics, starting with the publication in 1965 of Lotfi Asker Zadeh's seminal paper, Fuzzy Sets. The book begins with the basics of fuzzy mathematics before moving on to more complex topics, including: Fuzzy sets Fuzzy numbers Fuzzy relations Possibility theory Fuzzy abstract algebra And more Perfect for advanced undergraduate students, graduate students, and researchers with an interest in the field of fuzzy mathematics, A Modern Introduction to Fuzzy Mathematics walks through both foundational concepts and cutting-edge, new mathematics in the field.

Fuzzy Differential Equations in Various Approaches

Luciana Takata Gomes,Laécio Carvalho de Barros,Barnabas Bede
Fuzzy Differential Equations in Various Approaches Book PDF

Author : Luciana Takata Gomes,Laécio Carvalho de Barros,Barnabas Bede
Publisher : Springer
Page : 120 pages
File Size : 52,8 Mb
Release : 2015-09-07
Category : Mathematics
ISBN : 9783319225753

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Fuzzy Differential Equations in Various Approaches by Luciana Takata Gomes,Laécio Carvalho de Barros,Barnabas Bede Pdf

This book may be used as reference for graduate students interested in fuzzy differential equations and researchers working in fuzzy sets and systems, dynamical systems, uncertainty analysis, and applications of uncertain dynamical systems. Beginning with a historical overview and introduction to fundamental notions of fuzzy sets, including different possibilities of fuzzy differentiation and metric spaces, this book moves on to an overview of fuzzy calculus thorough exposition and comparison of different approaches. Innovative theories of fuzzy calculus and fuzzy differential equations using fuzzy bunches of functions are introduced and explored. Launching with a brief review of essential theories, this book investigates both well-known and novel approaches in this field; such as the Hukuhara differentiability and its generalizations as well as differential inclusions and Zadeh’s extension. Through a unique analysis, results of all these theories are examined and compared.

Fundamentals of Fuzzy Sets

Didier Dubois,Henri Prade
Fundamentals of Fuzzy Sets Book PDF

Author : Didier Dubois,Henri Prade
Publisher : Springer Science & Business Media
Page : 660 pages
File Size : 42,9 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.

Metamathematics of Fuzzy Logic

Petr Hájek
Metamathematics of Fuzzy Logic Book PDF

Author : Petr Hájek
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 52,7 Mb
Release : 2013-12-01
Category : Philosophy
ISBN : 9789401153003

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Metamathematics of Fuzzy Logic by Petr Hájek Pdf

This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. It aims to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named ‘fuzzy inference’ can be naturally understood as logical deduction. It is for mathematicians, logicians, computer scientists, specialists in artificial intelligence and knowledge engineering, and developers of fuzzy logic.

Mathematical Principles of Fuzzy Logic

Vilém Novák,Irina Perfilieva,J. Mockor
Mathematical Principles of Fuzzy Logic Book PDF

Author : Vilém Novák,Irina Perfilieva,J. Mockor
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461552178

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Mathematical Principles of Fuzzy Logic by Vilém Novák,Irina Perfilieva,J. Mockor Pdf

Mathematical Principles of Fuzzy Logic provides a systematic study of the formal theory of fuzzy logic. The book is based on logical formalism demonstrating that fuzzy logic is a well-developed logical theory. It includes the theory of functional systems in fuzzy logic, providing an explanation of what can be represented, and how, by formulas of fuzzy logic calculi. It also presents a more general interpretation of fuzzy logic within the environment of other proper categories of fuzzy sets stemming either from the topos theory, or even generalizing the latter. This book presents fuzzy logic as the mathematical theory of vagueness as well as the theory of commonsense human reasoning, based on the use of natural language, the distinguishing feature of which is the vagueness of its semantics.

Fuzzy Set Theory—and Its Applications

Hans-Jürgen Zimmermann
Fuzzy Set Theory and Its Applications Book PDF

Author : Hans-Jürgen Zimmermann
Publisher : Springer Science & Business Media
Page : 441 pages
File Size : 43,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401587020

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Fuzzy Set Theory—and Its Applications by Hans-Jürgen Zimmermann Pdf

Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.

Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems

Lotfi Asker Zadeh,George J. Klir,Bo Yuan
Fuzzy Sets Fuzzy Logic and Fuzzy Systems Book PDF

Author : Lotfi Asker Zadeh,George J. Klir,Bo Yuan
Publisher : World Scientific
Page : 848 pages
File Size : 52,5 Mb
Release : 1996
Category : Computers
ISBN : 9810224214

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Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems by Lotfi Asker Zadeh,George J. Klir,Bo Yuan Pdf

This book consists of selected papers written by the founder of fuzzy set theory, Lotfi A Zadeh. Since Zadeh is not only the founder of this field, but has also been the principal contributor to its development over the last 30 years, the papers contain virtually all the major ideas in fuzzy set theory, fuzzy logic, and fuzzy systems in their historical context. Many of the ideas presented in the papers are still open to further development. The book is thus an important resource for anyone interested in the areas of fuzzy set theory, fuzzy logic, and fuzzy systems, as well as their applications. Moreover, the book is also intended to play a useful role in higher education, as a rich source of supplementary reading in relevant courses and seminars.The book contains a bibliography of all papers published by Zadeh in the period 1949-1995. It also contains an introduction that traces the development of Zadeh's ideas pertaining to fuzzy sets, fuzzy logic, and fuzzy systems via his papers. The ideas range from his 1965 seminal idea of the concept of a fuzzy set to ideas reflecting his current interest in computing with words ? a computing in which linguistic expressions are used in place of numbers.Places in the papers, where each idea is presented can easily be found by the reader via the Subject Index.

An Introduction to Fuzzy Logic and Fuzzy Sets

James J. Buckley,Esfandiar Eslami
An Introduction to Fuzzy Logic and Fuzzy Sets Book PDF

Author : James J. Buckley,Esfandiar Eslami
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 47,5 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.

Fuzzy Sets, Fuzzy Logic, Applications

George Bojadziev,Maria Bojadziev
Fuzzy Sets Fuzzy Logic Applications Book PDF

Author : George Bojadziev,Maria Bojadziev
Publisher : World Scientific
Page : 304 pages
File Size : 40,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9810226063

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Fuzzy Sets, Fuzzy Logic, Applications by George Bojadziev,Maria Bojadziev Pdf

Fuzzy sets and fuzzy logic are powerful mathematical tools for modeling and controlling uncertain systems in industry, humanity, and nature; they are facilitators for approximate reasoning in decision making in the absence of complete and precise information. Their role is significant when applied to complex phenomena not easily described by traditional mathematics.The unique feature of the book is twofold: 1) It is the first introductory course (with examples and exercises) which brings in a systematic way fuzzy sets and fuzzy logic into the educational university and college system. 2) It is designed to serve as a basic text for introducing engineers and scientists from various fields to the theory of fuzzy sets and fuzzy logic, thus enabling them to initiate projects and make applications.

INTRODUCTION TO FUZZY SETS AND FUZZY LOGIC

M. GANESH
INTRODUCTION TO FUZZY SETS AND FUZZY LOGIC Book PDF

Author : M. GANESH
Publisher : PHI Learning Pvt. Ltd.
Page : 256 pages
File Size : 55,5 Mb
Release : 2006-01-01
Category : Mathematics
ISBN : 9788120328617

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INTRODUCTION TO FUZZY SETS AND FUZZY LOGIC by M. GANESH Pdf

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 in three parts. The concepts pertaining to the “crisp” situation such as Set Theory, Logic, Switching Function Theory and Boolean Algebra are covered in Part I of the text. Part II is devoted to fuzzy Set Theory, Fuzzy Relations and Fuzzy Logic. The applications of fuzzy set theory and fuzzy logic to Control Theory and Decision Making are designated Part III of the text. Designed as a textbook for the undergraduate and postgraduate students of Science and Engineering, the book will also be immensely useful to practicing engineers and computer scientists.

Mathematics of Fuzziness—Basic Issues

Xuzhu Wang,Da Ruan,Etienne E. Kerre
Mathematics of Fuzziness Basic Issues Book PDF

Author : Xuzhu Wang,Da Ruan,Etienne E. Kerre
Publisher : Springer
Page : 220 pages
File Size : 42,7 Mb
Release : 2009-03-11
Category : Mathematics
ISBN : 9783540783114

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Mathematics of Fuzziness—Basic Issues by Xuzhu Wang,Da Ruan,Etienne E. Kerre Pdf

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, fuzzy numbers, fuzzy algebra, fuzzy measures, fuzzy integrals, and fuzzy topology to fuzzy control in a strictly mathematical manner. It contains most of the authors’ research results in the field of fuzzy set theory and has evolved from the authors’ lecture notes to both undergraduate and graduate students over the last three decades. A lot of exercises in each chapter of the book are particularly suitable as a textbook for any undergraduate and graduate student in mathematics, computer science and engineering. The reading of the book will surely lay a solid foundation for further research on fuzzy set theory and its applications.