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Fuzzy logic is a wide, some would even say a wild, topic. Some years ago, on a trip to Vietnam, I found the label "Fuzzy Logic" prominently attached to the water heater in my hotel room. I can't imagine that, say, an epistemologist or an expert in modal logic, for that matter, will ever encounter the name of her research field attached to basic equipment of daily life. I mention this only to emphasize that any book about fuzzy logic, addressed to a general audience, has to face a wide range expectations, possibly also preconceptions in view of the controversies that accompanied the topic since its initiation by Lotfi A. Zadeh in the s.

In this section:

To browse Academia. Skip to main content. By using our site, you agree to our collection of information through the use of cookies. To learn more, view our Privacy Policy. Log In Sign Up. Download Free PDF. Fuzzy sets and fuzzy logic: Theory and applications: by George J.

Dan Simon. Download PDF. A short summary of this paper. The first part, containing Chapters , is concerned with the analysis and synthesis of linear systems, while the second part Chapters is devoted to the analysis and synthesis of nonlinear systems.

Chapter 1 gives a short survey of system theory: the Laplace transformation, Mason graphs of systems, transfer zeros, minimal polynomials, cyclic and noncyclic systems, stability, similarities of systems and polar factorization of transformation matrices. In Chapter 1, the systems are considered as fixed objects.

In Chapter 2, the parameters of the systems are closed intervals on the line of real numbers. The elements of the state matrix are not fixed points in R m, but belong to the parallel pipe limited by mT m-l edges. A group action is defined, and its main properties are proved. The Gershgorin theorem and the Jacobi theorem are given. In Chapters 3 and 4 the system is viewed as a control circuit. Chapter 3 is devoted to systems with single variable control. The change of the characteristic polynomial and adjoint matrix by feedback is discussed.

The Nyquist criterion and circle criterion are presented. A regulator containing a system copy is considered. The stability robustness of the stable control circuit is also considered. Chapters 4 and 5 deal with systems for multivariable control. Systems with multivariable control are introduced as systems given by the state matrix modified by a feedback matrix. For the solution of the basic problem of multivariable control, the eigenstructure is decomposed into a described part and a residual part.

The prescribed part of the eigenstructure should be robustly feasible; i. Six control circuits to change a given state matrix to some prescribed state matrix are introduced. To solve the problems, the method of action of the roots from Chapter 3 is used and further developed. An alternative approach to the solution of the stabilization for six control circuits is given in Chapter 5.

This approach is based on symmetry. In Chapter 5, a survey of classical matrix groups and algebras is presented. Chapter 6 gives a short survey of the basic notions and properties of nonlinear dynamic systems: the existence and uniqueness theorem for ordinary dif-ferential equations, manifolds, vector fields, stable, unstable and centre manifolds of the equilibrium point, hyperbolic dynamic systems, exact linearization of nonlinear dynamic systems, systems equivalence, stability of dynamic systems, Lyapunov's function approach and the centre manifold method.

Chapter 7 is devoted to systems with weakly nonlinear control dynamic systems with parameters defined locally around their equilibrium points. It concentrates on the classical control task--synthesis of nonlinear stable systems.

The synthesis of both hyperbolic and nonhyperbolic stable systems is considered. The common approximate linearization method for designing stable hyperbolic systems, and the centre manifold approach to design asymptotically stable nonhyperbolic systems, are used.

Systems with strongly nonlinear control are considered in Chapter 8. The chaotic behaviour of such systems, which is practically unpredictable, is discussed.

Some basic notions from dynamic system theory that are closely related to chaos are introduced. Three basic examples of chaotic systems Lorenz equations, a Roessler system and Chua's circuit are presented. A detailed characterization of chaos and the chaotic attractor is given. Active chaos creation is presented, using feedback control, which is called chaos synthesis. A new paradigm for the evaluation of the role of chaos in nature is given chaos is viewed as a positive phenomenon.

It is shown that control systems that cannot be stabilized in the usual sense may be stabilized to an attractor that is chaotic. The book is useful reading for anyone who is interested in robust control and in the chaotic behaviour of nonlinear systems. It is addressed, first of all, to graduate students specializing in control systems theory. It can also be recommended to practising engineers and applied scientists who are interested in robust control and chaos in nonlinear systems.

The book is broadly divided into two parts. The first part, which is primarily theoretical, presents a mathematically rigorous exposition of fuzzy systems. The second part presents various applications of fuzzy logic.

The text assumes a knowledge of probability and set theory, and is suitable for a one-or two-semester course at graduate level. Each chapter ends with a list of references and a set of problems. A solutions manual is available from the publisher. Fuzzy Sets and FuzzyThe theoretical half of the book consists of nine chapters.

Chapter 1 presents an interesting history of fuzzy-systems theory. It also presents an overview of both crisp sets and fuzzy sets. Chapter 2 discusses the relationship between crisp sets and fuzzy sets, including how fuzzy sets can be represented by combinations of crisp sets. It also shows how basic mathematical functions can be modified for application to fuzzy sets.

Chapter 3 covers the extension of the crisp complement, intersection, and union operations to fuzzy sets. It is shown that these operations as applied to fuzzy sets unlike their crisp counterparts, are not unique. There are, however, "standard" fuzzy operations which have special properties.

Chapter 3 also has a section on aggregation operations, which are combinations of several fuzzy sets to produce another fuzzy set.

Chapters 5 and 6 deal with fuzzy relations membership in fuzzy sets. Two fuzzy relations can be combined in a way that is similar to matrix multiplication, and inverse relations can be computed in a way that is analogous to matrix inversion. Chapter 7 introduces fuzzy measure theory, which deals with the degree of certainty of an element's membership of a crisp set. This chapter discusses three branches of fuzzy measure theory: evidence theory, possibility theory, and probability theory.

Chapter 8 gives an overview of multivalued logic and fuzzy logic, including fuzzy propositions and fuzzy inference. Chapter 9 is a fascinating discussion of information theory from the five different perspectives of classical set theory, fuzzyset theory, possibility theory, evidence theory, and probability theory. Chapter 17 is titled "MiscellaneousApplications", and discusses applications in fields such as medicine and economics. Following the main body of the text is a set of appendices which include overviews of neural networks, genetic algorithms, and rough sets.

The book contains an impressive bibliography of references. A mastery of the first theoretical half of this book would require a fairly high level of mathematical sophistication, and a significant expenditure of time and effort.

A reader looking for a simple, straightforward overview of fuzzy systems would be better served elsewhere. On the other hand, the second application half of the book is fairly independent of the first half, so an engineer could get a good feeling for fuzzy applications with only a basic understanding of the theory. In summary, this book is a complete and thorough exposition of fuzzy systems theory and application.

Anyone serious about becoming an expert in fuzzy systems, or contributing to the fuzzy systems literature, will find ample resources and direction in this book. I highly recommend it, both as a textbook and as a reference. The second half of the text considers a broad range of applications of fuzzy-systems theory.

The contrast between the theoretical orientation of the first half of the book and the applied orientation of the second half is immediately apparent. Chapter 10 is devoted to the construction of fuzzy membership functions. Membership functions can be constructed by humans who are experts in a given field, or they can be constructed on the basis of sample data. Chapter 11 shows how to build an expert system that uses fuzzy logic. Chapter 12 discusses the application of fuzzyset theory and fuzzy logic to systems theory.

The fuzzy systems that are discussed include fuzzy controllers, fuzzy neural networks, fuzzy state machines, and fuzzy dynamic systems. Chapter 13 gives an overview of fuzzy techniques for pattern recognition, and Chapter 14 discusses fuzzy databases and fuzzy information retrieval. Chapter 15 covers various aspects of fuzzy decision making This audience for this text is not very clearly targeted.

Kan includes software product managers, software development managers, software engineers, software product assurance personnel, and students in software engineering and in management information systems. On the other hand, he includes something for all of these audience sectors.

Metrics and Models in Software QualityChapter 1 deals, at excessive length, with the definition of software quality and total quality management TQM frameworks. Except for students, I think most of his audience should skip this chapter. Likewise, Chapter 2 is a too-long, non-detailed discussion of development approaches, process maturity, and standards. If this book were being used as an introductory text, perhaps the coverage would be appropriate.

For the person who needs this book, the software engineer and process modeler, the first two chapters are not useful. Logic: Theory and Applications, by George J. Related Papers. Dynamical Systems with Applications using Python Information. By Rony Pinedo Cordova.

Stability analysis results concerning the fuzzy control of a class of nonlinear time-varying systems.

On Measuring Uncertainty and Uncertainty-Based Information: Recent Developments

The classical view of concepts in psychology was challenged in the s when experimental evidence showed that concept categories are graded and thus cannot be represented adequately by classical sets. The possibility of using fuzzy set theory and fuzzy logic for representing and dealing with concepts was recognized initially but then virtually abandoned in the early s. In this volume, leading researchers—both psychologists working on concepts and mathematicians working on fuzzy logic—reassess the usefulness of fuzzy logic for the psychology of concepts. The book begins with two tutorials—one on concepts and the other on fuzzy logic—aimed at making relevant experimental and theoretical issues accessible to researchers in both fields. The contributors then discuss the experiments that led to the rejection of the classical view of concepts; analyze the various arguments against the use of fuzzy logic in the psychology of concepts and show that they are fallacious; review methods based on sound measurement principles for constructing fuzzy sets; introduce formal concept analysis and its capabilities when generalized by using fuzzy logic; consider conceptual combinations; examine lexical concepts; and propose a research program based on cooperation between researchers in the psychology of concepts and fuzzy logic. Skip to main content.

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Klir and B. Klir , B. Yuan Published Mathematics, Computer Science. Fuzzy Sets and Fuzzy Logic is a true magnum opus.

George Klir was born in in Prague , Czechoslovakia. In he received a M. In the early s he taught at the Institute of Computer Research in Prague. In he received a doctorate in computer science from the Czechoslovak Academy of Sciences. In the s Klir went to Iraq to teach at the Baghdad University for two years. At the end he managed to immigrate to the U.


Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets, Uncertainty, and Information—an earlier work of Professor Klir and Tina.


Fuzzy sets and fuzzy logic - theory and applications

It is shown in this paper how the emergence of fuzzy set theory and the theory of monotone measures considerably expanded the framework for formalizing uncertainty and suggested many new types of uncertainty theories. The paper focuses on issues regarding the measurement of the amount of relevant uncertainty predictive, prescriptive, diagnostic, etc. It is explained how information produced by an action can be measured by the reduction of uncertainty produced by the action.

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View larger cover. Reflecting the tremendous advances that have taken place in the study of fuzzy set theory and fuzzy logic from to the present, this book not only details the theoretical advances in these areas, but considers a broad variety of applications of fuzzy sets and fuzzy logic as well. Crisp Sets: An Overview. Fuzzy Sets: Basic Types.

Fuzzy sets and fuzzy logic - theory and applications

Fuzzy Sets and Fuzzy Logic Theory and Applications - George j. Klir , Bo Yuan

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It seems that you're in Germany. We have a dedicated site for Germany. Authors: Castillo , Oscar, Melin , Patricia. This book describes new methods for building intelligent systems using type-2 fuzzy logic and soft computing techniques. Soft Computing SC consists of several computing paradigms, including type-1 fuzzy logic, neural networks, and genetic algorithms, which can be used to create powerful hybrid intelligent systems.


by George J. Klir and Tina A. Folger. All rights Fuzzy Logic. Notes. 32 This is, in fact, precisely the basic concept of the fuzzy set, a concept that.


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Type-2 Fuzzy Logic: Theory and Applications

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David Z. 20.05.2021 at 23:21

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