On Logical Algebraic And Probabilistic Aspects Of Fuzzy Set Theory

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On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory

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Author : Susanne Saminger-Platz
Publisher : Springer
ISBN 13 : 3319288083
Total Pages : 275 pages
Book Rating : 4.3/5 (192 download)

Book Synopsis On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory by : Susanne Saminger-Platz

Download or read book On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory written by Susanne Saminger-Platz and published by Springer. This book was released on 2016-01-11 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of contributions by leading experts, developed around traditional themes discussed at the annual Linz Seminars on Fuzzy Set Theory. The different chapters have been written by former PhD students, colleagues, co-authors and friends of Peter Klement, a leading researcher and the organizer of the Linz Seminars on Fuzzy Set Theory. The book also includes advanced findings on topics inspired by Klement’s research activities, concerning copulas, measures and integrals, as well as aggregation problems. Some of the chapters reflect personal views and controversial aspects of traditional topics, while others deal with deep mathematical theories, such as the algebraic and logical foundations of fuzzy set theory and fuzzy logic. Originally thought as an homage to Peter Klement, the book also represents an advanced reference guide to the mathematical theories related to fuzzy logic and fuzzy set theory with the potential to stimulate important discussions on new research directions in the field.

Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms

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Author : Erich Peter Klement
Publisher : Elsevier
ISBN 13 : 0080459536
Total Pages : 491 pages
Book Rating : 4.0/5 (84 download)

Book Synopsis Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms by : Erich Peter Klement

Download or read book Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms written by Erich Peter Klement and published by Elsevier. This book was released on 2005-03-25 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gives a state of the art of triangular norms which can be used for the generalization of several mathematical concepts, such as conjunction, metric, measure, etc. 16 chapters written by leading experts provide a state of the art overview of theory and applications of triangular norms and related operators in fuzzy logic, measure theory, probability theory, and probabilistic metric spaces. Key Features: - Complete state of the art of the importance of triangular norms in various mathematical fields - 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications - Chapter authors are leading authorities in their fields - Triangular norms on different domains (including discrete, partially ordered) are described - Not only triangular norms but also related operators (aggregation operators, copulas) are covered - Book contains many enlightening illustrations · Complete state of the art of the importance of triangular norms in various mathematical fields · 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications · Chapter authors are leading authorities in their fields · Triangular norms on different domains (including discrete, partially ordered) are described · Not only triangular norms but also related operators (aggregation operators, copulas) are covered · Book contains many enlightening illustrations

Mathematics of Fuzzy Sets

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Author : Ulrich Höhle
Publisher : Springer Science & Business Media
ISBN 13 : 1461550793
Total Pages : 722 pages
Book Rating : 4.4/5 (615 download)

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.

Fuzzy Set Theory—and Its Applications

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Author : Hans-Jürgen Zimmermann
Publisher : Springer Science & Business Media
ISBN 13 : 9401006466
Total Pages : 526 pages
Book Rating : 4.4/5 (1 download)

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.

Fundamentals of Fuzzy Sets

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Author : Didier Dubois
Publisher : Springer Science & Business Media
ISBN 13 : 1461544297
Total Pages : 660 pages
Book Rating : 4.4/5 (615 download)

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.

Topological and Algebraic Structures in Fuzzy Sets

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Author : S.E. Rodabaugh
Publisher : Springer Science & Business Media
ISBN 13 : 9401702314
Total Pages : 468 pages
Book Rating : 4.4/5 (17 download)

Book Synopsis Topological and Algebraic Structures in Fuzzy Sets by : S.E. Rodabaugh

Download or read book Topological and Algebraic Structures in Fuzzy Sets written by S.E. Rodabaugh and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume summarizes recent developments in the topological and algebraic structures in fuzzy sets and may be rightly viewed as a continuation of the stan dardization of the mathematics of fuzzy sets established in the "Handbook", namely the Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Volume 3 of The Handbooks of Fuzzy Sets Series (Kluwer Academic Publish ers, 1999). Many of the topological chapters of the present work are not only based upon the foundations and notation for topology laid down in the Hand book, but also upon Handbook developments in convergence, uniform spaces, compactness, separation axioms, and canonical examples; and thus this work is, with respect to topology, a continuation of the standardization of the Hand book. At the same time, this work significantly complements the Handbook in regard to algebraic structures. Thus the present volume is an extension of the content and role of the Handbook as a reference work. On the other hand, this volume, even as the Handbook, is a culmination of mathematical developments motivated by the renowned International Sem inar on Fuzzy Set Theory, also known as the Linz Seminar, held annually in Linz, Austria. Much of the material of this volume is related to the Twenti eth Seminar held in February 1999, material for which the Seminar played a crucial and stimulating role, especially in providing feedback, connections, and the necessary screening of ideas.

Axiomatic Fuzzy Set Theory and Its Applications

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Author : Xiaodong Liu
Publisher : Springer
ISBN 13 : 3642004024
Total Pages : 514 pages
Book Rating : 4.6/5 (42 download)

Book Synopsis Axiomatic Fuzzy Set Theory and Its Applications by : Xiaodong Liu

Download or read book Axiomatic Fuzzy Set Theory and Its Applications written by Xiaodong Liu and published by Springer. This book was released on 2009-04-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that “fuzziness”—informationgranulesand fuzzy sets as one of its formal manifestations— is one of important characteristics of human cognitionandcomprehensionofreality. Fuzzy phenomena existinnature and are encountered quite vividly within human society. The notion of a fuzzy set has been introduced by L. A. , Zadeh in 1965 in order to formalize human concepts, in connection with the representation of human natural language and computing with words. Fuzzy sets and fuzzy logic are used for mod- ing imprecise modes of reasoning that play a pivotal role in the remarkable human abilities to make rational decisions in an environment a?ected by - certainty and imprecision. A growing number of applications of fuzzy sets originated from the “empirical-semantic” approach. From this perspective, we were focused on some practical interpretations of fuzzy sets rather than being oriented towards investigations of the underlying mathematical str- tures of fuzzy sets themselves. For instance, in the context of control theory where fuzzy sets have played an interesting and practically relevant function, the practical facet of fuzzy sets has been stressed quite signi?cantly. However, fuzzy sets can be sought as an abstract concept with all formal underpinnings stemming from this more formal perspective. In the context of applications, it is worth underlying that membership functions do not convey the same meaning at the operational level when being cast in various contexts.

Non-Classical Logics and their Applications to Fuzzy Subsets

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Author : Ulrich Höhle
Publisher : Springer Science & Business Media
ISBN 13 : 9401102155
Total Pages : 391 pages
Book Rating : 4.4/5 (11 download)

Book Synopsis Non-Classical Logics and their Applications to Fuzzy Subsets by : Ulrich Höhle

Download or read book Non-Classical Logics and their Applications to Fuzzy Subsets written by Ulrich Höhle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-Classical Logics and their Applications to Fuzzy Subsets is the first major work devoted to a careful study of various relations between non-classical logics and fuzzy sets. This volume is indispensable for all those who are interested in a deeper understanding of the mathematical foundations of fuzzy set theory, particularly in intuitionistic logic, Lukasiewicz logic, monoidal logic, fuzzy logic and topos-like categories. The tutorial nature of the longer chapters, the comprehensive bibliography and index make it suitable as a valuable and important reference for graduate students as well as research workers in the field of non-classical logics. The book is arranged in three parts: Part A presents the most recent developments in the theory of Heyting algebras, MV-algebras, quantales and GL-monoids. Part B gives a coherent and current account of topos-like categories for fuzzy set theory based on Heyting algebra valued sets, quantal sets of M-valued sets. Part C addresses general aspects of non-classical logics including epistemological problems as well as recursive properties of fuzzy logic.

Mathematics of Fuzzy Sets

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Author : Ulrich Höhle
Publisher : Springer
ISBN 13 : 9781461550808
Total Pages : 716 pages
Book Rating : 4.5/5 (58 download)

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. This book was released on 2012-01-10 with total page 716 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.

Fuzzy Set Theory and Its Applications

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Author : H. J. Zimmerman
Publisher : Allied Publishers
ISBN 13 : 9788170235255
Total Pages : 430 pages
Book Rating : 4.2/5 (352 download)

Book Synopsis Fuzzy Set Theory and Its Applications by : H. J. Zimmerman

Download or read book Fuzzy Set Theory and Its Applications written by H. J. Zimmerman and published by Allied Publishers. This book was released on 1996 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Truth Value Algebra of Type-2 Fuzzy Sets

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Author : John Harding
Publisher : CRC Press
ISBN 13 : 1498735290
Total Pages : 251 pages
Book Rating : 4.4/5 (987 download)

Book Synopsis The Truth Value Algebra of Type-2 Fuzzy Sets by : John Harding

Download or read book The Truth Value Algebra of Type-2 Fuzzy Sets written by John Harding and published by CRC Press. This book was released on 2016-03-30 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Type-2 fuzzy sets extend both ordinary and interval-valued fuzzy sets to allow distributions, rather than single values, as degrees of membership. Computations with these truth values are governed by the truth value algebra of type-2 fuzzy sets. The Truth Value Algebra of Type-2 Fuzzy Sets: Order Convolutions of Functions on the Unit Interval explo

A First Course in Fuzzy Logic

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Author : Hung T. Nguyen
Publisher : CRC Press
ISBN 13 : 0429012608
Total Pages : 192 pages
Book Rating : 4.4/5 (29 download)

Book Synopsis A First Course in Fuzzy Logic by : Hung T. Nguyen

Download or read book A First Course in Fuzzy Logic written by Hung T. Nguyen and published by CRC Press. This book was released on 2018-12-07 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course in Fuzzy Logic, Fourth Edition is an expanded version of the successful third edition. It provides a comprehensive introduction to the theory and applications of fuzzy logic. This popular text offers 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 applications. New in the Fourth Edition: Features new results on fuzzy sets of type-2 Provides more information on copulas for modeling dependence structures Includes quantum probability for uncertainty modeling in social sciences, especially in economics With its comprehensive updates, this new edition presents all the background necessary for students, instructors and professionals to begin using fuzzy logic in its many—applications in computer science, mathematics, statistics, and engineering. About the Authors: Hung T. Nguyen is a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. He is also an Adjunct Professor of Economics at Chiang Mai University, Thailand. Carol L. Walker is also a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. Elbert A. Walker is a Professor Emeritus, Department of Mathematical Sciences, New Mexico State University.

Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems

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Author : Lotfi Asker Zadeh
Publisher : World Scientific
ISBN 13 : 9789810224219
Total Pages : 848 pages
Book Rating : 4.2/5 (242 download)

Book Synopsis Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems by : Lotfi Asker Zadeh

Download or read book Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems written by Lotfi Asker Zadeh and published by World Scientific. This book was released on 1996 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

On Intuitionistic Fuzzy Sets Theory

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Author : Krassimir T. Atanassov
Publisher : Springer
ISBN 13 : 3642291279
Total Pages : 328 pages
Book Rating : 4.6/5 (422 download)

Book Synopsis On Intuitionistic Fuzzy Sets Theory by : Krassimir T. Atanassov

Download or read book On Intuitionistic Fuzzy Sets Theory written by Krassimir T. Atanassov and published by Springer. This book was released on 2012-04-28 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to be a comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the author ́s previous book on Intuitionistic Fuzzy Sets, published by Springer in 1999 (Atanassov, Krassimir T., Intuitionistic Fuzzy Sets, Studies in Fuzziness and soft computing, ISBN 978-3-7908-1228-2, 1999). Since the aforementioned book has appeared, the research activity of the author within the area of intuitionistic fuzzy sets has been expanding into many directions. The results of the author ́s most recent work covering the past 12 years as well as the newest general ideas and open problems in this field have been therefore collected in this new book.

Fuzzy Set Theory

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Author : George J. Klir
Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.3/5 (91 download)

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.

Fuzzy Logic and Probability Applications

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Author : Timothy J. Ross
Publisher : SIAM
ISBN 13 : 0898715253
Total Pages : 424 pages
Book Rating : 4.8/5 (987 download)

Book Synopsis Fuzzy Logic and Probability Applications by : Timothy J. Ross

Download or read book Fuzzy Logic and Probability Applications written by Timothy J. Ross and published by SIAM. This book was released on 2002-01-01 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shows both the shortcomings and benefits of each technique, and even demonstrates useful combinations of the two.

Fuzzy Mathematics

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Author : Etienne E. Kerre
Publisher : MDPI
ISBN 13 : 303897322X
Total Pages : 287 pages
Book Rating : 4.0/5 (389 download)

Book Synopsis Fuzzy Mathematics by : Etienne E. Kerre

Download or read book Fuzzy Mathematics written by Etienne E. Kerre and published by MDPI. This book was released on 2018-11-28 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Fuzzy Mathematics" that was published in Mathematics