Fuzzy Set Theory

Author : George J. Klir,Ute H. St. Clair,Bo Yuan
Publisher : Unknown
Page : 264 pages
File Size : 52,9 Mb
Release : 1997
Category : Computers
ISBN : UOM:39015041012140

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Fuzzy Set Theory by George J. Klir,Ute H. St. Clair,Bo Yuan Pdf

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.

Author : R. Lowen
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401587419

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Fuzzy Set Theory by R. Lowen Pdf

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.

Author : Hans-Jürgen Zimmermann
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 53,5 Mb
Release : 2013-03-09
Category : Business & Economics
ISBN : 9789401579490

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Fuzzy Set Theory — and Its Applications by Hans-Jürgen Zimmermann Pdf

Since its inception 20 years ago the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of this theory can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, pattern recognition, robotics and others. Theoretical advances, too, have been made in many directions, and a gap has arisen between advanced theoretical topics and applications, which often use the theory at a rather elementary level. The primary goal of this book is to close this gap - to provide a textbook for courses in fuzzy set theory and a book that can be used as an introduction. This revised book updates the research agenda, with the chapters of possibility theory, fuzzy logic and approximate reasoning, expert systems and control, decision making and fuzzy set models in operations research being restructured and rewritten. Exercises have been added to almost all chapters and a teacher's manual is available upon request.

Author : Bhargava A.K.
Publisher : S. Chand Publishing
Page : 128 pages
File Size : 54,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9788121941945

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Fuzzy Set Theory Fuzzy Logic and their Applications by Bhargava A.K. Pdf

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 : Valerie V. Cross,Thomas A. Sudkamp
Publisher : Physica
Page : 207 pages
File Size : 46,9 Mb
Release : 2013-06-05
Category : Mathematics
ISBN : 9783790817935

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Similarity and Compatibility in Fuzzy Set Theory by Valerie V. Cross,Thomas A. Sudkamp Pdf

Assessing the degree to which two objects, an object and a query, or two concepts are similar or compatible is a fundamental component of human reasoning and consequently is critical in the development of automated diagnosis, classification, information retrieval and decision systems. The assessment of similarity has played an important role in such diverse disciplines such as taxonomy, psychology, and the social sciences. Each discipline has proposed methods for quantifying similarity judgments suitable for its particular applications. This book presents a unified approach to quantifying similarity and compatibility within the framework of fuzzy set theory and examines the primary importance of these concepts in approximate reasoning. Examples of the application of similarity measures in various areas including expert systems, information retrieval, and intelligent database systems are provided.

Author : Hans-Jürgen Zimmermann
Publisher : Springer Science & Business Media
Page : 441 pages
File Size : 53,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401587020

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Fuzzy Set Theory—and Its Applications by Hans-Jürgen Zimmermann Pdf

Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with 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. All chapters have been updated. Exercises are included.

Author : Michael Smithson,Jay Verkuilen
Publisher : SAGE
Page : 116 pages
File Size : 53,7 Mb
Release : 2006-02-17
Category : Mathematics
ISBN : 076192986X

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Fuzzy Set Theory by Michael Smithson,Jay Verkuilen Pdf

This book introduces fuzzy set theory to social science researchers. Fuzzy sets are categories with blurred boundaries. With classical sets, objects are either in the set or not, but objects can belong partially to more than one fuzzy set at a time. Many concepts in the social sciences have this characteristic, and fuzzy set theory provides methods for systematically dealing with them. A primary reason for not going beyond programmatic statements and rather unsophisticated uses of fuzzy set theory has been the lack of practical methods for combining fuzzy set concepts with statistical methods. This monograph takes that topic as its major focus, and provides explicit guides for researchers who would like to harness fuzzy set concepts while being able to make statistical inferences and test their models. Real examples and data-sets from several disciplines illustrate the techniques and applications, demonstrating how a combination of fuzzy sets and statistics enable researchers to analyze their data in new ways.

Author : Zeshui Xu
Publisher : Springer
Page : 474 pages
File Size : 44,8 Mb
Release : 2014-01-30
Category : Technology & Engineering
ISBN : 9783319047119

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Hesitant Fuzzy Sets Theory by Zeshui Xu Pdf

This book provides the readers with a thorough and systematic introduction to hesitant fuzzy theory. It presents the most recent research results and advanced methods in the field. These includes: hesitant fuzzy aggregation techniques, hesitant fuzzy preference relations, hesitant fuzzy measures, hesitant fuzzy clustering algorithms and hesitant fuzzy multi-attribute decision making methods. Since its introduction by Torra and Narukawa in 2009, hesitant fuzzy sets have become more and more popular and have been used for a wide range of applications, from decision-making problems to cluster analysis, from medical diagnosis to personnel appraisal and information retrieval. This book offers a comprehensive report on the state-of-the-art in hesitant fuzzy sets theory and applications, aiming at becoming a reference guide for both researchers and practitioners in the area of fuzzy mathematics and other applied research fields (e.g. operations research, information science, management science and engineering) characterized by uncertain ("hesitant") information. Because of its clarity and self contained explanations, the book can also be adopted as a textbook from graduate and advanced undergraduate students.

Author : Krassimir T. Atanassov
Publisher : Physica
Page : 336 pages
File Size : 47,6 Mb
Release : 2013-03-20
Category : Mathematics
ISBN : 9783790818703

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Intuitionistic Fuzzy Sets by Krassimir T. Atanassov Pdf

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.

Author : André Jones,Arnold Kaufmann,Hans-Jürgen Zimmermann
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400946828

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Fuzzy Sets Theory and Applications by André Jones,Arnold Kaufmann,Hans-Jürgen Zimmermann Pdf

Problems in decision making and in other areas such as pattern recogni tion, control, structural engineering etc. involve numerous aspects of uncertainty. Additional vagueness is introduced as models become more complex but not necessarily more meaningful by the added details. During the last two decades one has become more and more aware of the fact that not all this uncertainty is of stochastic (random) cha racter and that, therefore, it can not be modelled appropriately by probability theory. This becomes the more obvious the more we want to represent formally human knowledge. As far as uncertain data are concerned, we have neither instru ments nor reasoning at our disposal as well defined and unquestionable as those used in the probability theory. This almost infallible do main is the result of a tremendous work by the whole scientific world. But when measures are dubious, bad or no longer possible and when we really have to make use of the richness of human reasoning in its variety, then the theories dealing with the treatment of uncertainty, some quite new and other ones older, provide the required complement, and fill in the gap left in the field of knowledge representation. Nowadays, various theories are widely used: fuzzy sets, belief function, the convenient associations between probability and fuzzines~ etc ••• We are more and more in need of a wide range of instruments and theories to build models that are more and more adapted to the most complex systems.

Author : Chander Mohan
Publisher : MV Learning
Page : 128 pages
File Size : 49,7 Mb
Release : 2019-06-30
Category : Technology & Engineering
ISBN : 9388971019

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An Introduction to Fuzzy Set Theory and Fuzzy Logic by Chander Mohan Pdf

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.

Author : Ulrich Höhle,S.E. Rodabaugh
Publisher : Springer Science & Business Media
Page : 722 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461550792

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Mathematics of Fuzzy Sets by Ulrich Höhle,S.E. Rodabaugh Pdf

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.

Author : Barnabas Bede
Publisher : Springer
Page : 281 pages
File Size : 45,8 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.

Author : Madan M. Gupta,Rammohan K. Ragade,Ronald R. Yager
Publisher : North-Holland
Page : 772 pages
File Size : 54,8 Mb
Release : 1979
Category : Mathematics
ISBN : MINN:319510009994689

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Advances in Fuzzy Set Theory and Applications by Madan M. Gupta,Rammohan K. Ragade,Ronald R. Yager Pdf

Author : James J. Buckley,Esfandiar Eslami
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 48,5 Mb
Release : 2013-11-11
Category : Computers
ISBN : 9783790817997

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An Introduction to Fuzzy Logic and Fuzzy Sets by James J. Buckley,Esfandiar Eslami Pdf

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.