Author: George Metcalfe
Publisher: Springer Science & Business Media
ISBN: 1402094094
Category : Mathematics
Languages : en
Pages : 279
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Book Description
Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations.
Author: Radim Bělohlávek
Publisher: Oxford University Press
ISBN: 0190200014
Category : Mathematics
Languages : en
Pages : 545
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Book Description
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.
Author: Ofer Arieli
Publisher: Springer Nature
ISBN: 3030712583
Category : Philosophy
Languages : en
Pages : 369
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Book Description
This book is a collection of contributions honouring Arnon Avron’s seminal work on the semantics and proof theory of non-classical logics. It includes presentations of advanced work by some of the most esteemed scholars working on semantic and proof-theoretical aspects of computer science logic. Topics in this book include frameworks for paraconsistent reasoning, foundations of relevance logics, analysis and characterizations of modal logics and fuzzy logics, hypersequent calculi and their properties, non-deterministic semantics, algebraic structures for many-valued logics, and representations of the mechanization of mathematics. Avron’s foundational and pioneering contributions have been widely acknowledged and adopted by the scientific community. His research interests are very broad, spanning over proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of logic in computer science and artificial intelligence. This is clearly reflected by the diversity of topics discussed in the chapters included in this book, all of which directly relate to Avron’s past and present works. This book is of interest to computer scientists and scholars of formal logic.
Author: George J. Klir
Publisher:
ISBN: 9789332549425
Category :
Languages : en
Pages : 574
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Book Description
Author: Petr Cintula
Publisher:
ISBN: 9781848901933
Category : Mathematics
Languages : en
Pages : 384
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Book Description
Originating as an attempt to provide solid logical foundations for fuzzy set theory, and motivated also by philosophical and computational problems of vagueness and imprecision, Mathematical Fuzzy Logic (MFL) has become a significant subfield of mathematical logic. Research in this area focuses on many-valued logics with linearly ordered truth values and has yielded elegant and deep mathematical theories and challenging problems, thus continuing to attract an ever increasing number of researchers. This handbook provides, through its several volumes, an up-to-date systematic presentation of the best-developed areas of MFL. Its intended audience is researchers working on MFL or related fields, that may use the text as a reference book, and anyone looking for a comprehensive introduction to MFL. This handbook will be useful not only for readers interested in pure mathematical logic, but also for those interested in logical foundations of fuzzy set theory or in a mathematical apparatus suitable for dealing with some philosophical and linguistic issues related to vagueness. This third volume starts with three chapters on semantics of fuzzy logics, namely, on the structure of linearly ordered algebras, on semantic games, and on Ulam-Renyi games; it continues with an introduction to fuzzy logics with evaluated syntax, a survey of fuzzy description logics, and a study of probability on MV-algebras; and it ends with a philosophical chapter on the role of fuzzy logics in theories of vagueness."
Author: Kazuo Tanaka
Publisher: Springer
ISBN: 0387948074
Category : Computers
Languages : en
Pages : 148
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Book Description
Fuzzy logic has become an important tool for a number of different applications ranging from the control of engineering systems to artificial intelligence. In this concise introduction, the author presents a succinct guide to the basic ideas of fuzzy logic, fuzzy sets, fuzzy relations, and fuzzy reasoning, and shows how they may be applied. The book culminates in a chapter which describes fuzzy logic control: the design of intelligent control systems using fuzzy if-then rules which make use of human knowledge and experience to behave in a manner similar to a human controller. Throughout, the level of mathematical knowledge required is kept basic and the concepts are illustrated with numerous diagrams to aid in comprehension. As a result, all those curious to know more about fuzzy concepts and their real-world application will find this a good place to start.
Author: Zhenyuan Wang
Publisher: Springer Science & Business Media
ISBN: 0387768521
Category : Mathematics
Languages : en
Pages : 392
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Book Description
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.
Author: Bhargava A.K.
Publisher: S. Chand Publishing
ISBN: 8121941946
Category : Science
Languages : en
Pages : 400
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Book Description
Classical Sets Fuzzy Relation Equations Basic Concepts On Fuzzy Sets Possibility Theory Fuzzy Sets Versus Crisp Sets Fuzzy Logic Operations On Fuzzy Sets Uncertainty-Based Information Interval Arithmetic Approximate Reasoning Fuzzy Numbers And Fuzzy Arithmetic Fuzzy Control And Fuzzy Expert Systems Fuzzy Relations Fuzzy Decision Making Index
Author: George J Klir
Publisher: World Scientific
ISBN: 9814499811
Category : Computers
Languages : en
Pages : 842
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Book Description
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.
Author: Hung T. Nguyen
Publisher: CRC Press
ISBN: 1420057103
Category : Computers
Languages : en
Pages : 436
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Book Description
A First Course in Fuzzy Logic, Third Edition continues to provide the ideal introduction to the theory and applications of fuzzy logic. This best-selling text provides a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world a
