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Concepts Of Fuzzy Mathematics
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Book Synopsis Fuzzy Mathematical Concepts by : S. Nanda
Download or read book Fuzzy Mathematical Concepts written by S. Nanda and published by Alpha Science International, Limited. This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy Mathematical Concepts discusses the theory and applications of fuzzy sets, fuzzy relations, fuzzy logic and rough sets including the theory and applications to algebra, topology, analysis, probability, and measure theory. While the first two chapters deal with basic theory and the prerequisite for the rest of the book, readers interested in algebra and logic may go through chapters 3 and 4, those interested in topology may proceed to chapters 5 to 8, and for analysis one may read chapters 8 and 9. Readers interested in Rough Set Theory may directly proceed to chapter 10 after completing chapters 1 and 2. A part of the book can be covered in one semester depending on the requirement and the whole book in two semesters.
Book Synopsis A Modern Introduction to Fuzzy Mathematics by : Apostolos Syropoulos
Download or read book A Modern Introduction to Fuzzy Mathematics written by Apostolos Syropoulos and published by John Wiley & Sons. This book was released on 2020-07-28 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fuzzy Logic and Mathematics by : Radim Bělohlávek
Download or read book Fuzzy Logic and Mathematics written by Radim Bělohlávek and published by Oxford University Press. This book was released on 2017 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fuzzy Mathematics by : John N. Mordeson
Download or read book Fuzzy Mathematics written by John N. Mordeson and published by Physica. This book was released on 2012-11-08 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the mid-1960's I had the pleasure of attending a talk by Lotfi Zadeh at which he presented some of his basic (and at the time, recent) work on fuzzy sets. Lotfi's algebra of fuzzy subsets of a set struck me as very nice; in fact, as a graduate student in the mid-1950's, I had suggested similar ideas about continuous-truth-valued propositional calculus (inffor "and", sup for "or") to my advisor, but he didn't go for it (and in fact, confused it with the foundations of probability theory), so I ended up writing a thesis in a more conventional area of mathematics (differential algebra). I especially enjoyed Lotfi's discussion of fuzzy convexity; I remember talking to him about possible ways of extending this work, but I didn't pursue this at the time. I have elsewhere told the story of how, when I saw C. L. Chang's 1968 paper on fuzzy topological spaces, I was impelled to try my hand at fuzzi fying algebra. This led to my 1971 paper "Fuzzy groups", which became the starting point of an entire literature on fuzzy algebraic structures. In 1974 King-Sun Fu invited me to speak at a U. S. -Japan seminar on Fuzzy Sets and their Applications, which was to be held that summer in Berkeley.
Book Synopsis Fuzzy Set Theory by : George J. Klir
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.
Book Synopsis Mathematics of Fuzzy Sets by : Ulrich Höhle
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.
Book Synopsis An Introduction to Fuzzy Logic and Fuzzy Sets by : James J. Buckley
Download or read book An Introduction to Fuzzy Logic and Fuzzy Sets written by James J. Buckley and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis INTRODUCTION TO FUZZY SETS AND FUZZY LOGIC by : M. GANESH
Download or read book INTRODUCTION TO FUZZY SETS AND FUZZY LOGIC written by M. GANESH and published by PHI Learning Pvt. Ltd.. This book was released on 2006-01-01 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Concepts of Fuzzy Mathematics by : Manoranjan Kumar Singh
Download or read book Concepts of Fuzzy Mathematics written by Manoranjan Kumar Singh and published by Springer Nature. This book was released on with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematics of Fuzziness—Basic Issues by : Xuzhu Wang
Download or read book Mathematics of Fuzziness—Basic Issues written by Xuzhu Wang and published by Springer. This book was released on 2009-03-11 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Data Engineering by : Olaf Wolkenhauer
Download or read book Data Engineering written by Olaf Wolkenhauer and published by John Wiley & Sons. This book was released on 2004-04-07 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although data engineering is a multi-disciplinary field withapplications in control, decision theory, and the emerging hot areaof bioinformatics, there are no books on the market that make thesubject accessible to non-experts. This book fills the gap in thefield, offering a clear, user-friendly introduction to the maintheoretical and practical tools for analyzing complex systems. Anftp site features the corresponding MATLAB and Mathematical toolsand simulations. Market: Researchers in data management, electrical engineering,computer science, and life sciences.
Book Synopsis An Introduction to Fuzzy Set Theory and Fuzzy Logic by : Chander Mohan
Download or read book An Introduction to Fuzzy Set Theory and Fuzzy Logic written by Chander Mohan and published by MV Learning. This book was released on 2019-06-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the rudiments of fuzzy set theory and fuzzy logic and related topics and their applications in a simple and easy-to-understand manner. The book avoids the extremes of abstract mathematical proofs as well as specialized technical details of different areas of application.
Book Synopsis Fuzzy Set Theory—and Its Applications by : Hans-Jürgen Zimmermann
Download or read book Fuzzy Set Theory—and Its Applications written by Hans-Jürgen Zimmermann and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 set models in operations research. Existing material has been updated, and extended exercises are included.
Book Synopsis A Modern Introduction to Fuzzy Mathematics by : Apostolos Syropoulos
Download or read book A Modern Introduction to Fuzzy Mathematics written by Apostolos Syropoulos and published by John Wiley & Sons. This book was released on 2020-07-01 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Fundamentals of Fuzzy Sets by : Didier Dubois
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.
Book Synopsis Generalized Measure Theory by : Zhenyuan Wang
Download or read book Generalized Measure Theory written by Zhenyuan Wang and published by Springer Science & Business Media. This book was released on 2010-07-07 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Measure Theory examines the relatively new mathematical area of generalized measure theory. The exposition unfolds systematically, beginning with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory. Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate level in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A sound background in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to researchers working in the emerging area of generalized measure theory.
