Handbook Of Mathematical Fuzzy Logic

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Handbook of Mathematical Fuzzy Logic

Petr Cintula,Christian G Fermueller,Carles Noguera
Handbook of Mathematical Fuzzy Logic Book PDF

Author : Petr Cintula,Christian G Fermueller,Carles Noguera
Publisher : Unknown
Page : 384 pages
File Size : 54,8 Mb
Release : 2015-12-31
Category : Mathematics
ISBN : 1848901933

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Handbook of Mathematical Fuzzy Logic by Petr Cintula,Christian G Fermueller,Carles Noguera Pdf

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."

Mathematics of Fuzzy Sets and Fuzzy Logic

Barnabas Bede
Mathematics of Fuzzy Sets and Fuzzy Logic Book PDF

Author : Barnabas Bede
Publisher : Springer
Page : 276 pages
File Size : 44,8 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.

Petr Hájek on Mathematical Fuzzy Logic

Franco Montagna
Petr H jek on Mathematical Fuzzy Logic Book PDF

Author : Franco Montagna
Publisher : Springer
Page : 318 pages
File Size : 43,8 Mb
Release : 2014-09-23
Category : Mathematics
ISBN : 9783319062334

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Petr Hájek on Mathematical Fuzzy Logic by Franco Montagna Pdf

This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vagueness, building connections between Hájek's favorite fuzzy logic and linguistic models of vagueness. Other articles introduce alternative notions of consequence relation, namely, the preservation of truth degrees, which is discussed in a general context, and the differential semantics. For the latter, a surprisingly strong standard completeness theorem is proved. Another contribution also looks at two principles valid in classical logic and characterize the three main t-norm logics in terms of these principles. Other articles, with an algebraic flavour, offer a summary of the applications of lattice ordered-groups to many-valued logic and to quantum logic, as well as an investigation of prelinearity in varieties of pointed lattice ordered algebras that satisfy a weak form of distributivity and have a very weak implication. The last part of the volume contains an article on possibilistic modal logics defined over MTL chains, a topic that Hájek discussed in his celebrated work, Metamathematics of Fuzzy Logic, and another one where the authors, besides offering unexpected premises such as proposing to call Hájek's basic fuzzy logic HL, instead of BL, propose a very weak system, called SL as a candidate for the role of the really basic fuzzy logic. The paper also provides a generalization of the prelinearity axiom, which was investigated by Hájek in the context of fuzzy logic.

Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures

Jana, Chiranjibe,Senapati, Tapan,Pal, Madhumangal
Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures Book PDF

Author : Jana, Chiranjibe,Senapati, Tapan,Pal, Madhumangal
Publisher : IGI Global
Page : 439 pages
File Size : 46,5 Mb
Release : 2019-10-25
Category : Mathematics
ISBN : 9781799801924

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Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures by Jana, Chiranjibe,Senapati, Tapan,Pal, Madhumangal Pdf

In the world of mathematics, the study of fuzzy relations and its theories are well-documented and a staple in the area of calculative methods. What many researchers and scientists overlook is how fuzzy theory can be applied to industries outside of arithmetic. The framework of fuzzy logic is much broader than professionals realize. There is a lack of research on the full potential this theoretical model can reach. The Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures provides emerging research exploring the theoretical and practical aspects of fuzzy set theory and its real-life applications within the fields of engineering and science. Featuring coverage on a broad range of topics such as complex systems, topological spaces, and linear transformations, this book is ideally designed for academicians, professionals, and students seeking current research on innovations in fuzzy logic in algebra and other matrices.

Handbook of Mathematical Logic

J. Barwise
Handbook of Mathematical Logic Book PDF

Author : J. Barwise
Publisher : Elsevier
Page : 1164 pages
File Size : 49,7 Mb
Release : 1982-03-01
Category : Computers
ISBN : 9780080933641

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Handbook of Mathematical Logic by J. Barwise Pdf

The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.

Handbook of Fuzzy Computation

E Ruspini,P Bonissone,W Pedrycz
Handbook of Fuzzy Computation Book PDF

Author : E Ruspini,P Bonissone,W Pedrycz
Publisher : CRC Press
Page : 1229 pages
File Size : 41,8 Mb
Release : 2020-03-05
Category : Computers
ISBN : 9781420050394

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Handbook of Fuzzy Computation by E Ruspini,P Bonissone,W Pedrycz Pdf

Initially conceived as a methodology for the representation and manipulation of imprecise and vague information, fuzzy computation has found wide use in problems that fall well beyond its originally intended scope of application. Many scientists and engineers now use the paradigms of fuzzy computation to tackle problems that are either intractable

Handbook of Research on Advances and Applications of Fuzzy Sets and Logic

Broumi, Said
Handbook of Research on Advances and Applications of Fuzzy Sets and Logic Book PDF

Author : Broumi, Said
Publisher : IGI Global
Page : 944 pages
File Size : 53,9 Mb
Release : 2022-03-04
Category : Mathematics
ISBN : 9781799879817

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Handbook of Research on Advances and Applications of Fuzzy Sets and Logic by Broumi, Said Pdf

Fuzzy logic, which is based on the concept of fuzzy set, has enabled scientists to create models under conditions of imprecision, vagueness, or both at once. As a result, it has now found many important applications in almost all sectors of human activity, becoming a complementary feature and supporter of probability theory, which is suitable for modelling situations of uncertainty derived from randomness. Fuzzy mathematics has also significantly developed at the theoretical level, providing important insights into branches of traditional mathematics like algebra, analysis, geometry, topology, and more. With such widespread applications, fuzzy sets and logic are an important area of focus in mathematics. The Handbook of Research on Advances and Applications of Fuzzy Sets and Logic studies recent theoretical advances of fuzzy sets and numbers, fuzzy systems, fuzzy logic and their generalizations, extensions, and more. This book also explores the applications of fuzzy sets and logic applied to science, technology, and everyday life to further provide research on the subject. This book is ideal for mathematicians, physicists, computer specialists, engineers, practitioners, researchers, academicians, and students who are looking to learn more about fuzzy sets, fuzzy logic, and their applications.

Non-Classical Logics and their Applications to Fuzzy Subsets

Ulrich Höhle,Erich Peter Klement
Non Classical Logics and their Applications to Fuzzy Subsets Book PDF

Author : Ulrich Höhle,Erich Peter Klement
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401102155

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Non-Classical Logics and their Applications to Fuzzy Subsets by Ulrich Höhle,Erich Peter Klement Pdf

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.

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

Susanne Saminger-Platz,Radko Mesiar
On Logical Algebraic and Probabilistic Aspects of Fuzzy Set Theory Book PDF

Author : Susanne Saminger-Platz,Radko Mesiar
Publisher : Springer
Page : 275 pages
File Size : 46,7 Mb
Release : 2016-01-11
Category : Technology & Engineering
ISBN : 9783319288086

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On Logical, Algebraic, and Probabilistic Aspects of Fuzzy Set Theory by Susanne Saminger-Platz,Radko Mesiar Pdf

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.

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 : 300 pages
File Size : 51,7 Mb
Release : 1996-01-09
Category : Computers
ISBN : 9789814499941

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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.

Springer Handbook of Computational Intelligence

Janusz Kacprzyk,Witold Pedrycz
Springer Handbook of Computational Intelligence Book PDF

Author : Janusz Kacprzyk,Witold Pedrycz
Publisher : Springer
Page : 1634 pages
File Size : 41,7 Mb
Release : 2015-05-28
Category : Technology & Engineering
ISBN : 9783662435052

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Springer Handbook of Computational Intelligence by Janusz Kacprzyk,Witold Pedrycz Pdf

The Springer Handbook for Computational Intelligence is the first book covering the basics, the state-of-the-art and important applications of the dynamic and rapidly expanding discipline of computational intelligence. This comprehensive handbook makes readers familiar with a broad spectrum of approaches to solve various problems in science and technology. Possible approaches include, for example, those being inspired by biology, living organisms and animate systems. Content is organized in seven parts: foundations; fuzzy logic; rough sets; evolutionary computation; neural networks; swarm intelligence and hybrid computational intelligence systems. Each Part is supervised by its own Part Editor(s) so that high-quality content as well as completeness are assured.

Handbook of Philosophical Logic

Dov M. Gabbay,Franz Guenthner
Handbook of Philosophical Logic Book PDF

Author : Dov M. Gabbay,Franz Guenthner
Publisher : Springer Science & Business Media
Page : 417 pages
File Size : 43,5 Mb
Release : 2013-03-09
Category : Philosophy
ISBN : 9789401704526

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Handbook of Philosophical Logic by Dov M. Gabbay,Franz Guenthner Pdf

It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as weIl as to consumers of logic in many applied areas. The main logic artiele in the Encyelopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good. ! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook 0/ Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook 0/ Philosophical Logic, published 1983-1989 came at a fortunate at the evolution of logic. This was the time when logic temporal junction was gaining ground in computer science and artificial intelligence cireles. These areas were under increasing commercial pressure to provide devices which help andjor replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.

Fuzzy Logic Handbook

Frank West
Fuzzy Logic Handbook Book PDF

Author : Frank West
Publisher : Unknown
Page : 0 pages
File Size : 54,9 Mb
Release : 2015-02-19
Category : Fuzzy logic
ISBN : 1632382113

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Fuzzy Logic Handbook by Frank West Pdf

Fuzzy logic has developed into an important means of solving problems in all domains. It has a huge impact on the design of autonomous intelligent systems. This book discusses hybrid algorithms, techniques, and implementations of fuzzy logic. The main focus of the book is on the models and fundamentals of fuzzy logic and issues related to its technique and implementations. This book will prove beneficial to engineers, researchers, and graduate students who are working in the field of fuzzy logic.

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 : 49,9 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 Logic of Quasi-Truth: An Algebraic Treatment

Antonio Di Nola,Revaz Grigolia,Esko Turunen
Fuzzy Logic of Quasi Truth An Algebraic Treatment Book PDF

Author : Antonio Di Nola,Revaz Grigolia,Esko Turunen
Publisher : Springer
Page : 116 pages
File Size : 43,5 Mb
Release : 2016-03-18
Category : Technology & Engineering
ISBN : 9783319304069

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Fuzzy Logic of Quasi-Truth: An Algebraic Treatment by Antonio Di Nola,Revaz Grigolia,Esko Turunen Pdf

This book presents the first algebraic treatment of quasi-truth fuzzy logic and covers the algebraic foundations of many-valued logic. It offers a comprehensive account of basic techniques and reports on important results showing the pivotal role played by perfect many-valued algebras (MV-algebras). It is well known that the first-order predicate Łukasiewicz logic is not complete with respect to the canonical set of truth values. However, it is complete with respect to all linearly ordered MV –algebras. As there are no simple linearly ordered MV-algebras in this case, infinitesimal elements of an MV-algebra are allowed to be truth values. The book presents perfect algebras as an interesting subclass of local MV-algebras and provides readers with the necessary knowledge and tools for formalizing the fuzzy concept of quasi true and quasi false. All basic concepts are introduced in detail to promote a better understanding of the more complex ones. It is an advanced and inspiring reference-guide for graduate students and researchers in the field of non-classical many-valued logics.