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Author: R. Lowen
Publisher: Springer Science & Business Media
ISBN: 9401587418
Category : Mathematics
Languages : en
Pages : 415
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Book Description
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: R. Lowen
Publisher: Springer Science & Business Media
ISBN: 9401587418
Category : Mathematics
Languages : en
Pages : 415
Get Book Here
Book Description
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: 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: Michael Smithson
Publisher: SAGE
ISBN: 9780761929864
Category : Mathematics
Languages : en
Pages : 116
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Book Description
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: Hans-Jürgen Zimmermann
Publisher: Springer Science & Business Media
ISBN: 9401579490
Category : Business & Economics
Languages : en
Pages : 408
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Book Description
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: 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: I. Burhan Türksen
Publisher: Elsevier
ISBN: 0080525717
Category : Computers
Languages : en
Pages : 543
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Book Description
Fuzzy set and logic theory suggest that all natural language linguistic expressions are imprecise and must be assessed as a matter of degree. But in general membership degree is an imprecise notion which requires that Type 2 membership degrees be considered in most applications related to human decision making schemas. Even if the membership functions are restricted to be Type1, their combinations generate an interval – valued Type 2 membership. This is part of the general result that Classical equivalences breakdown in Fuzzy theory. Thus all classical formulas must be reassessed with an upper and lower expression that are generated by the breakdown of classical formulas.Key features:- Ontological grounding- Epistemological justification- Measurement of Membership- Breakdown of equivalences- FDCF is not equivalent to FCCF- Fuzzy Beliefs- Meta-Linguistic axioms- Ontological grounding- Epistemological justification- Measurement of Membership- Breakdown of equivalences- FDCF is not equivalent to FCCF- Fuzzy Beliefs- Meta-Linguistic axioms
Author: George J. Klir
Publisher:
ISBN: 9789332549425
Category :
Languages : en
Pages : 574
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Book Description
Author: Barnabas Bede
Publisher: Springer
ISBN: 3642352219
Category : Technology & Engineering
Languages : en
Pages : 281
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Book Description
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: Valerie V. Cross
Publisher: Physica
ISBN: 3790817937
Category : Mathematics
Languages : en
Pages : 207
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Book Description
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: Krassimir T. Atanassov
Publisher: Physica
ISBN: 3790818704
Category : Mathematics
Languages : en
Pages : 336
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Book Description
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.
