Intuitionistic Fuzzy Logics

by Krassimir T. Atanassov

Author	: Krassimir T. Atanassov
Publisher	: Springer
Total Pages	: 144
Release	: 2016-12-10
Genre	: Technology & Engineering
ISBN	: 3319489534

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The book offers a comprehensive survey of intuitionistic fuzzy logics. By reporting on both the author’s research and others’ findings, it provides readers with a complete overview of the field and highlights key issues and open problems, thus suggesting new research directions. Starting with an introduction to the basic elements of intuitionistic fuzzy propositional calculus, it then provides a guide to the use of intuitionistic fuzzy operators and quantifiers, and lastly presents state-of-the-art applications of intuitionistic fuzzy sets. The book is a valuable reference resource for graduate students and researchers alike.

Intuitionistic Fuzzy Sets

by Krassimir T. Atanassov

Author	: Krassimir T. Atanassov
Publisher	: Physica
Total Pages	: 336
Release	: 2013-03-20
Genre	: Mathematics
ISBN	: 3790818704

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In the beginning of 1983, I came across A. Kaufmann's book "Introduction to the theory of fuzzy sets" (Academic Press, New York, 1975). This was my first acquaintance with the fuzzy set theory. Then I tried to introduce a new component (which determines the degree of non-membership) in the definition of these sets and to study the properties of the new objects so defined. I defined ordinary operations as "n", "U", "+" and "." over the new sets, but I had began to look more seriously at them since April 1983, when I defined operators analogous to the modal operators of "necessity" and "possibility". The late George Gargov (7 April 1947 - 9 November 1996) is the "god father" of the sets I introduced - in fact, he has invented the name "intu itionistic fuzzy", motivated by the fact that the law of the excluded middle does not hold for them. Presently, intuitionistic fuzzy sets are an object of intensive research by scholars and scientists from over ten countries. This book is the first attempt for a more comprehensive and complete report on the intuitionistic fuzzy set theory and its more relevant applications in a variety of diverse fields. In this sense, it has also a referential character.

Recent Advances in Intuitionistic Fuzzy Logic Systems and Mathematics

by Said Melliani

Author	: Said Melliani
Publisher	:
Total Pages	: 0
Release	: 2021
Genre	:
ISBN	: 9783030539306

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This book provides an overview of the state-of-the-art in both the theory and methods of intuitionistic fuzzy logic, partial differential equations and numerical methods in informatics. Covering topics such as fuzzy intuitionistic Hilbert spaces, intuitionistic fuzzy differential equations, fuzzy intuitionistic metric spaces, and numerical methods for differential equations, it discusses applications such as fuzzy real-time scheduling, intelligent control, diagnostics and time series prediction. The book features selected contributions presented at the 6th international congress of the Moroccan Applied Mathematics Society, which took place at Sultan Moulay Slimane University Beni Mellal, Morocco, from 7 to 9 November 2019.

On Intuitionistic Fuzzy Sets Theory

by Krassimir T. Atanassov

Author	: Krassimir T. Atanassov
Publisher	: Springer
Total Pages	: 328
Release	: 2012-04-28
Genre	: Technology & Engineering
ISBN	: 3642291279

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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.

Interval-Valued Intuitionistic Fuzzy Sets

by Krassimir T. Atanassov

Author	: Krassimir T. Atanassov
Publisher	: Springer Nature
Total Pages	: 205
Release	: 2019-09-21
Genre	: Technology & Engineering
ISBN	: 3030320901

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The book offers a comprehensive survey of interval-valued intuitionistic fuzzy sets. It reports on cutting-edge research carried out by the founder of the intuitionistic fuzzy sets, Prof. Krassimir Atanassov, giving a special emphasis to the practical applications of this extension. A few interesting case studies, such as in the area of data mining, decision making and pattern recognition, among others, are discussed in detail. The book offers the first comprehensive guide on interval-valued intuitionistic fuzzy sets. By providing the readers with a thorough survey and important practical details, it is expected to support them in carrying out applied research and to encourage them to test the theory behind the sets for new advanced applications. The book is a valuable reference resource for graduate students and researchers alike.

Type-2 Fuzzy Logic: Theory and Applications

by Oscar Castillo

Author	: Oscar Castillo
Publisher	: Springer Science & Business Media
Total Pages	: 252
Release	: 2008-02-20
Genre	: Mathematics
ISBN	: 3540762833

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This book describes new methods for building intelligent systems using type-2 fuzzy logic and soft computing (SC) techniques. The authors extend the use of fuzzy logic to a higher order, which is called type-2 fuzzy logic. Combining type-2 fuzzy logic with traditional SC techniques, we can build powerful hybrid intelligent systems that can use the advantages that each technique offers. This book is intended to be a major reference tool and can be used as a textbook.

Recent Advances in Intuitionistic Fuzzy Logic Systems

by Said Melliani

Author	: Said Melliani
Publisher	: Springer
Total Pages	: 320
Release	: 2018-10-09
Genre	: Technology & Engineering
ISBN	: 3030021556

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This book aims at providing an overview of state-of-the-art in both the theory and methods of intuitionistic fuzzy logic, partial differential equations and numerical methods in informatics. It covers topics such as fuzzy intuitionistic Hilbert spaces, intuitionistic fuzzy differential equations, fuzzy intuitionistic metric spaces, and numerical methods for differential equations. It reports on applications such as fuzzy real time scheduling, intelligent control, diagnostics and time series prediction. Chapters were carefully selected among contributions presented at the second edition of the International Conference on Intuitionistic Fuzzy Sets and Mathematical Science, ICIFSMAS, held on April 11-13, 2018, at Al Akhawayn University of Ifrane, in Morocco.

Logical Options

by John L. Bell

Author	: John L. Bell
Publisher	: Broadview Press
Total Pages	: 313
Release	: 2001-03-30
Genre	: Philosophy
ISBN	: 1551112973

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Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some classical first-order logic and would like to learn about other logics important to their philosophical work.

Fuzzy Set and Its Extension

by Tamalika Chaira

Author	: Tamalika Chaira
Publisher	: John Wiley & Sons
Total Pages	: 304
Release	: 2019-03-21
Genre	: Technology & Engineering
ISBN	: 1119544211

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Provides detailed mathematical exposition of the fundamentals of fuzzy set theory, including intuitionistic fuzzy sets This book examines fuzzy and intuitionistic fuzzy mathematics and unifies the latest existing works in literature. It enables readers to fully understand the mathematics of both fuzzy set and intuitionistic fuzzy set so that they can use either one in their applications. Each chapter of Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set begins with an introduction, theory, and several examples to guide readers along. The first one starts by laying the groundwork of fuzzy/intuitionistic fuzzy sets, fuzzy hedges, and fuzzy relations. The next covers fuzzy numbers and explains Zadeh's extension principle. Then comes chapters looking at fuzzy operators; fuzzy similarity measures and measures of fuzziness; and fuzzy/intuitionistic fuzzy measures and fuzzy integrals. The book also: discusses the definition and properties of fuzzy measures; examines matrices and determinants of a fuzzy matrix; and teaches about fuzzy linear equations. Readers will also learn about fuzzy subgroups. The second to last chapter examines the application of fuzzy and intuitionistic fuzzy mathematics in image enhancement, segmentation, and retrieval. Finally, the book concludes with coverage the extension of fuzzy sets. This book: Covers both fuzzy and intuitionistic fuzzy sets and includes examples and practical applications Discusses intuitionistic fuzzy integrals and recent aggregation operators using Choquet integral, with examples Includes a chapter on applications in image processing using fuzzy and intuitionistic fuzzy sets Explains fuzzy matrix operations and features examples Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set is an ideal text for graduate and research students, as well as professionals, in image processing, decision-making, pattern recognition, and control system design.