Fuzzy Set Theory—and Its Applications

Author: Hans-Jürgen Zimmermann

Publisher: Springer Science & Business Media

ISBN: 9401587027

Category: Mathematics

Page: 435

View: 6891

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.

Fuzzy Set Theory—and Its Applications

Author: Hans-Jürgen Zimmermann

Publisher: Springer Science & Business Media

ISBN: 9780792374350

Category: Business & Economics

Page: 514

View: 3734

Since its inception, the theory of fuzzy sets has advanced in a variety of ways and in many disciplines. Applications of fuzzy technology can be found in artificial intelligence, computer science, control engineering, decision theory, expert systems, logic, management science, operations research, robotics, and others. Theoretical advances have been made in many directions. The primary goal of Fuzzy Set Theory - and its Applications, Fourth Edition is to provide a textbook for courses in fuzzy set theory, and a book that can be used as an introduction. To balance the character of a textbook with the dynamic nature of this research, many useful references have been added to develop a deeper understanding for the interested reader. Fuzzy Set Theory - and its Applications, Fourth Edition updates the research agenda 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. Chapters have been updated and extended exercises are included.

Fuzzy Set Theory—and Its Applications

Author: Hans-Jürgen Zimmermann

Publisher: Springer Science & Business Media

ISBN: 9401587027

Category: Mathematics

Page: 435

View: 3946

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.

Axiomatic Fuzzy Set Theory and Its Applications

Author: Xiaodong Liu,Witold Pedrycz

Publisher: Springer Science & Business Media

ISBN: 3642004016

Category: Computers

Page: 514

View: 3274

This volume examines Axiomatic Fuzzy Sets (AFS), in which fuzzy sets and probability are treated in a unified and coherent fashion. It presents AFS as a rigorous mathematical theory as well as a flexible methodology for the development of intelligent systems.

Intuitionistic Fuzzy Sets

Theory and Applications

Author: Krassimir T. Atanassov

Publisher: Physica

ISBN: 3790818704

Category: Mathematics

Page: 324

View: 5050

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.

Metric Spaces of Fuzzy Sets

Theory and Applications

Author: Phil Diamond,Peter E. Kloeden

Publisher: World Scientific

ISBN: 9789810217310

Category: Mathematics

Page: 178

View: 3681

The primary aim of the book is to provide a systematic development of the theory of metric spaces of normal, upper semicontinuous fuzzy convex fuzzy sets with compact support sets, mainly on the base space ?n. An additional aim is to sketch selected applications in which these metric space results and methods are essential for a thorough mathematical analysis.This book is distinctly mathematical in its orientation and style, in contrast with many of the other books now available on fuzzy sets, which, although all making use of mathematical formalism to some extent, are essentially motivated by and oriented towards more immediate applications and related practical issues. The reader is assumed to have some previous undergraduate level acquaintance with metric spaces and elementary functional analysis.

Fuzzy Set Theory

Foundations and Applications

Author: George J. Klir,Ute H. St. Clair,Bo Yuan

Publisher: N.A

ISBN: 9780133410587

Category: Computers

Page: 245

View: 8242

This book is designed to help anyone understand the basics of fuzzy sets, whether or not they have a mathematical background. The book first presents a basic grounding in information theory, classical logic and set theories. Next, it introduces the basics of fuzzy sets, distinguishing them from traditional crisp sets, and introducing the concept of membership function. The distinctions between classical and fuzzy relations are introduced, as are representations of fuzzy relations; fuzzy equivalence relations; fuzzy partial orderings, and related topics. The book introduces fuzzy arithmetic and fuzzy numbers. It also presents a detailed introduction to fuzzy logic, multivalued logics, fuzzy propositions, quantifiers, linguistic hedges and approximate reasoning. Several basic and advanced applications for fuzzy set theory are presented as well. Any non-technical reader interested in fuzzy sets and fuzzy logic. Also ideal for introductory level-students, whether they are planning a technical or non-technical course of study.

Similarity and Compatibility in Fuzzy Set Theory

Assessment and Applications

Author: Valerie V. Cross,Thomas A. Sudkamp

Publisher: Springer Science & Business Media

ISBN: 9783790814583

Category: Computers

Page: 209

View: 786

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.

Fuzzy Set Theory

Applications in the Social Sciences

Author: Michael Smithson,Jay Verkuilen

Publisher: SAGE

ISBN: 9780761929864

Category: Mathematics

Page: 97

View: 2691

Fuzzy set theory deals with sets or categories whose boundaries are blurry or, in other words, "fuzzy." This book presents an accessible introduction to fuzzy set theory, focusing on its applicability to the social sciences. Unlike most books on this topic, Fuzzy Set Theory: Applications in the Social Sciences provides a systematic, yet practical guide for researchers wishing to combine fuzzy set theory with standard statistical techniques and model-testing.

Fuzzy sets and their applications

Author: Vilém Novák

Publisher: Taylor & Francis

ISBN: N.A

Category: Mathematics

Page: 248

View: 4811

A systematic treatise of fuzzy set theory and of some of its applications, containing many of the author's original results together with those of other Czech scientists. Intended for researchers, teachers and students of artificial intelligence, computational linguistics, system engineering, modelling and control of industrial processes, decision-making and management sciences, mathematics and logic, knowledge engineering and expert systems.

Fuzzy Sets, Decision Making, and Expert Systems

Author: Hans-Jürgen Zimmermann

Publisher: Springer Science & Business Media

ISBN: 9400932499

Category: Business & Economics

Page: 336

View: 3560

In the two decades since its inception by L. Zadeh, the theory of fuzzy sets has matured into a wide-ranging collection of concepts, models, and tech niques for dealing with complex phenomena which do not lend themselves to analysis by classical methods based on probability theory and bivalent logic. Nevertheless, a question which is frequently raised by the skeptics is: Are there, in fact, any significant problem areas in which the use of the theory of fuzzy sets leads to results which could not be obtained by classical methods? The approximately 5000 publications in this area, which are scattered over many areas such as artificial intelligence, computer science, control engineering, decision making, logic, operations research, pattern recognition, robotics and others, provide an affirmative answer to this question. In spite of the large number of publications, good and comprehensive textbooks which could facilitate the access of newcomers to this area and support teaching were missing until recently. To help to close this gap and to provide a textbook for courses in fuzzy set theory which can also be used as an introduction to this field, the first volume ofthis book was published in 1985 [Zimmermann 1985 b]. This volume tried to cover fuzzy set theory and its applications as extensively as possible. Applications could, therefore, only be described to a limited extent and not very detailed.

Fuzzy Set Theory and Advanced Mathematical Applications

Author: Da Ruan

Publisher: Springer Science & Business Media

ISBN: 1461523575

Category: Mathematics

Page: 324

View: 4671

Fuzzy Set Theory and Advanced Mathematical Applications contains contributions by many of the leading experts in the field, including coverage of the mathematical foundations of the theory, decision making and systems science, and recent developments in fuzzy neural control. The book supplies a readable, practical toolkit with a clear introduction to fuzzy set theory and its evolution in mathematics and new results on foundations of fuzzy set theory, decision making and systems science, and fuzzy control and neural systems. Each chapter is self-contained, providing up-to-date coverage of its subject. Audience: An important reference work for university students, and researchers and engineers working in both industrial and academic settings.

Fuzzy Set Theory

Basic Concepts, Techniques and Bibliography

Author: R. Lowen

Publisher: Springer Science & Business Media

ISBN: 9401587418

Category: Mathematics

Page: 408

View: 3499

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.

Mathematics of Fuzzy Sets and Fuzzy Logic

Author: Barnab'as Bede

Publisher: Springer

ISBN: 3642352219

Category: Computers

Page: 276

View: 9570

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.

The Fuzzification of Systems

The Genesis of Fuzzy Set Theory and its Initial Applications - Developments up to the 1970s

Author: Rudolf Seising

Publisher: Springer

ISBN: 3540717951

Category: Computers

Page: 412

View: 4951

Today, Fuzzy Set Theory is the core discipline of so-called ‘soft’ computing, and provides new impetus for research in the field of artificial intelligence. In this fascinating book, the history of Fuzzy Set Theory and the ways it was first used are incorporated into the history of 20th century science and technology. Influences from philosophy, system theory and cybernetics stemming from the earliest part of the 20th century are considered alongside those of communication and control theory from mid-century.

Fuzzy Sets & their Application to Clustering & Training

Author: Beatrice Lazzerini,Lakhmi C. Jain,D. Dumitrescu

Publisher: CRC Press

ISBN: 9780849305894

Category: Computers

Page: 664

View: 9108

Fuzzy set theory - and its underlying fuzzy logic - represents one of the most significant scientific and cultural paradigms to emerge in the last half-century. Its theoretical and technological promise is vast, and we are only beginning to experience its potential. Clustering is the first and most basic application of fuzzy set theory, but forms the basis of many, more sophisticated, intelligent computational models, particularly in pattern recognition, data mining, adaptive and hierarchical clustering, and classifier design. Fuzzy Sets and their Application to Clustering and Training offers a comprehensive introduction to fuzzy set theory, focusing on the concepts and results needed for training and clustering applications. It provides a unified mathematical framework for fuzzy classification and clustering, a methodology for developing training and classification methods, and a general method for obtaining a variety of fuzzy clustering algorithms. The authors - top experts from around the world - combine their talents to lay a solid foundation for applications of this powerful tool, from the basic concepts and mathematics through the study of various algorithms, to validity functionals and hierarchical clustering. The result is Fuzzy Sets and their Application to Clustering and Training - an outstanding initiation into the world of fuzzy learning classifiers and fuzzy clustering.

Applications of Fuzzy Set Theory in Human Factors

Author: W. Karwowski,A. Mital

Publisher: Elsevier

ISBN: 1483294366

Category: Technology & Engineering

Page: 471

View: 2396

The development of the theory of fuzzy sets was motivated largely by the need for a computational framework for dealing with systems in which human judgement, behavior and emotions play a dominant role. Although there are very few papers on fuzzy sets in the literature of psychology and cognitive science, the theory of fuzzy sets provides a much better model for human cognition than traditional approaches. By focusing on the application of fuzzy sets in human factors, this book provides a valuable, authoritative overview of what the theory is about and how it can be applied. An impressive feature is the broad spectrum of applications, ranging from the use of fuzzy methods in the ergonomic diagnostics of industrial production systems to approximate reasoning in risk analysis and the modeling of human-computer interactions in information retrieval tasks. Equally impressive is the very wide variety of disciplines and countries represented by the contributors.