Fuzzy Set Theory—and Its Applications

Author: Hans-Jürgen Zimmermann

Publisher: Springer Science & Business Media

ISBN: 9401006466

Category: Mathematics

Page: 514

View: 2336

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This introduction to fuzzy set theory and its multitude of applications seeks to balance the character of the book with the dynamic nature of the research. This edition includes new 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. Existing material has been updated, and extended exercises are included.
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Intuitionistic Fuzzy Sets

Theory and Applications

Author: Krassimir T. Atanassov

Publisher: Physica

ISBN: 3790818704

Category: Mathematics

Page: 324

View: 1703

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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.
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Fuzzy Set Theory Fuzzy Logic and their Applications

Author: Bhargava A.K.

Publisher: S. Chand Publishing

ISBN: 8121941946

Category: Mathematics

Page: N.A

View: 347

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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
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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: 9366

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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.
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Axiomatic Fuzzy Set Theory and Its Applications

Author: Xiaodong Liu,Witold Pedrycz

Publisher: Springer Science & Business Media

ISBN: 3642004016

Category: Mathematics

Page: 514

View: 1451

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It is well known that “fuzziness”—informationgranulesand fuzzy sets as one of its formal manifestations— is one of important characteristics of human cognitionandcomprehensionofreality. Fuzzy phenomena existinnature and are encountered quite vividly within human society. The notion of a fuzzy set has been introduced by L. A. , Zadeh in 1965 in order to formalize human concepts, in connection with the representation of human natural language and computing with words. Fuzzy sets and fuzzy logic are used for mod- ing imprecise modes of reasoning that play a pivotal role in the remarkable human abilities to make rational decisions in an environment a?ected by - certainty and imprecision. A growing number of applications of fuzzy sets originated from the “empirical-semantic” approach. From this perspective, we were focused on some practical interpretations of fuzzy sets rather than being oriented towards investigations of the underlying mathematical str- tures of fuzzy sets themselves. For instance, in the context of control theory where fuzzy sets have played an interesting and practically relevant function, the practical facet of fuzzy sets has been stressed quite signi?cantly. However, fuzzy sets can be sought as an abstract concept with all formal underpinnings stemming from this more formal perspective. In the context of applications, it is worth underlying that membership functions do not convey the same meaning at the operational level when being cast in various contexts.
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Metric Spaces of Fuzzy Sets: Theory and Applications

Author: Phil Diamond,Peter Kloeden

Publisher: World Scientific

ISBN: 9814518115

Category: Computers

Page: 188

View: 7171

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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 ℜn. 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. Contents:Fuzzy SetsSpaces of Subsets of ℜnCompact Convex Subsets of ℜnSet Valued MappingsCrisp GeneralizationsThe Space εnMetrics on εnCompactness CriteriaGeneralizationsFuzzy Set Valued Mappings of Real VariablesFuzzy Random VariablesComputational MethodsFuzzy Differential EquationsOptimization Under UncertaintyFuzzy Iterations and Image Processing Readership: Mathematicians and computer scientists. keywords:Metric Spaces;Multifunctions;Fuzzy Sets;Fuzzy Data Fitting;Fuzzy Dynamical Systems;Iterated Fuzzy Systems “… is a valuable addition to the literature about fuzzy analysis, leading the reader to the edge of current research.” Mathematical Reviews “… the book seems to be the only, and thus valuable, source of mathematical concepts and results on fuzzy sets and functions, which are presented in a clear, and quite rigorous, format.” Journal of Classification
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Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems

Selected Papers

Author: Lotfi Asker Zadeh,George J. Klir,Bo Yuan

Publisher: World Scientific

ISBN: 9789810224219

Category: Computers

Page: 826

View: 5500

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This book consists of selected papers written by the founder of fuzzy set theory, Lotfi A Zadeh. Since Zadeh is not only the founder of this field, but has also been the principal contributor to its development over the last 30 years, the papers contain virtually all the major ideas in fuzzy set theory, fuzzy logic, and fuzzy systems in their historical context. Many of the ideas presented in the papers are still open to further development. The book is thus an important resource for anyone interested in the areas of fuzzy set theory, fuzzy logic, and fuzzy systems, as well as their applications. Moreover, the book is also intended to play a useful role in higher education, as a rich source of supplementary reading in relevant courses and seminars.The book contains a bibliography of all papers published by Zadeh in the period 1949-1995. It also contains an introduction that traces the development of Zadeh's ideas pertaining to fuzzy sets, fuzzy logic, and fuzzy systems via his papers. The ideas range from his 1965 seminal idea of the concept of a fuzzy set to ideas reflecting his current interest in computing with words ? a computing in which linguistic expressions are used in place of numbers.Places in the papers, where each idea is presented can easily be found by the reader via the Subject Index.
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Machine Intelligence

Quo Vadis?

Author: Peter Sincak,Kaoru Hirota,J n Vas?c? k

Publisher: World Scientific

ISBN: 9789812562531

Category: Artificial intelligence

Page: 458

View: 2967

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This book brings together the contributions of leading researchers inthe field of machine intelligence, covering areas such as fuzzy logic, neural networks, evolutionary computation and hybrid systems.There is wide coverage of the subject from simple tools, throughindustrial applications, to applications in high-level intelligentsystems which are biologically motivated, such as humanoid robots (andselected parts of these systems, like the visual cortex). Readers willgain a comprehensive overview of the issues in machine intelligence, afield which promises to play a very important role in the informationsociety of the future
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