# FUZZY SETS AND FUZZY LOGIC THEORY AND APPLICATIONS EBOOK

FUZZY SETS AND FUZZY LOGIC Theory and ApplicationsGEORGE J. KLIR AND BO YUANFor baoic and boastDre faarmatlart. -n. fuzzy sets and fuzzy logic. Pages·· MB·5, Downloads. FUZZY SETS AND FUZZY LOGIC. Theory and Applications. GEORGE J. KLIR AND BO. Fuzzy Sets and Fuzzy Logic: Theory and Applications with ISBN is a book written by George J. Klir, Bo Yuan. We have this.

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The primary purpose of this book is to provide the reader with a comprehensive coverage of theoretical foundations of fuzzy set theory and fuzzy logic, as well as . Fuzzy Sets and Fuzzy Logic Theory and Applications - George j. Klir, Bo Yuan - Free ebook download as PDF File .pdf), Text File .txt) or read book online for. 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 .

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Basic concepts of fuzzy relations are introduced in Chapter 5 and employed in Chapter 6 for the study of fuzzy relation equations, an important tool for many applications of fuzzy set theory. Preface xiv Figure El Prerequisite dependencies among chapters of this book.

The position of possibility theory within the broader framework of fuzzy measure theory is also examined. Chapter 8 overviews basic aspects of fuzzy logic, including its connection to classical naultivalued logics, the various types of fuzzy propositions, and basic types of fuzzy inference rules. Chapter 9, the last chapter in Part I, is devoted to the examination of the connection between uncertainty and information, as represented by fuzzy sets, possibility theory, or evidence theory.

The chapter shows how relevant uncertainty and uncertainty-based information can be measured and how these uncertainty measures can be utilized.

Part IL which is devoted to applications of fuzzy set theory and fuzzy logic, cons ists of the remaining eight chapters. Chapter 10 cgainincs various methods for constructing membership functions of fuzzy sets, including the increasingly popular use of neural networks. Chapter 11 is devoted to the use of fuzzy logic for approximate reasoning in expert systems.

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

It includes a thorough examination of the concept of a fuzzy implication. Fuzzy systems are covered in Chapter 12, including fuzzy controllers, fuzzy automata, and fuzzy neural networks.

Fuzzy techniques in the related areas of clustering. Fuzzy databases, a well developed application area of fuzzy set theory, and the related area of fuzzy retrieval systems are covered in Chapter Basic ideas of the various types of fuzzy decision making are summarized in Chapter Engineering applications other than fuzzy control are touched upon in Chapter 16, and applications in various other areas medicine, economics, etc.

The prerequisite dependencies among the individual chapters and some appendices are expressed by the diagram in Fig.

Following the diagram, the reader has ample flexibility ill studying the material. For example, Chapters 3, 5 and 6 may be studied prior to Chapters 2 and 4; Chapter 10 and Appendix A may be studies prior to Chapter 2 and Chapters 4 through 9; etc. In order to avoid interruptions in the main text, virtually all bibliographical, his bark:al, and other remarks are incorporated in the notes that follow each individual chapter.

These notes are uniquely numbered and are only occasionally referred to in the text.

At the graduate level, on the other hand, we encourage coverage of most of these proofs in order to effect a deeper understanding of the material. In all cases, the relevance of the material to the specific area of student interest can be emphasized with additional applicationoriented readings guided by relevant notes in Part H of the text.

Each chapter is followed by a set of exercises, which are intended to enhance an understanding of the material presented in the chapter. The solutions to a selected subset of these exercises are provided in the instructor's manual, which also contains further suggestions for use of the text under various circumstances.

The book contains an extensive bibliography, which covers virtually all relevant books and significant papers published prior to It also contains a Bibliographical Index, which consists of reference lists for selected application areas and theoretical topics.

This index should be particularly useful for graduate, preiect-oriented courses, as well as for both practitioners and researchers.

## George J. Klir/Bo YklSIt

Each book in the bibliography is emphasized by printing its year of publication in bold. In science, this change bas been manifested by a gradual transition from the traditional view, which insists that uncertainty is undesirable in science and should be avoided by all possible means, to an alternative view, which is tolerant of uncertainty and insists that science cannot avoid it.

The first stage of the transition from the traditional view to the modern view of uncertainty began in the late 19th century, when physics became concerned with processes at the molecular level. The need for a fundamentally different approach to the study of physical processes at the molecular level motivated the development of relevant statistical methods, which turned out to be applicable not only to the study of molecular processes statistical mechanics , but.

In statistical methods, specific manifestations of microscopic entities molecules, individual telephone sites, ete. These two types of methods are thus highly complementary. When one type excels, the other totally fails. Despite their complernentarity, these types of methods cover, unfortunately, only problems that are clustered around the two extremes of complexity arid randomness scales.

In his well-known paper, Warren Weaver [] refers to them as problems of organized simplicity and asorganized complexity. He argues that these types of problems represent only a tiny fraction of all syStems problems.

Most problems are somewhere between these two extremes: they involve nonlinear systems with large numbers of components and rich interactions among the components, which are -usually nondeterrainistic, but not as a result of randomness that could yield meaningful statistical averages. Weavercalls them problems of organized complccity; they are typical in life, cognitive, social, and environmental sciences, as well as in applied fields such as modem technology or medicine.

The emergence of computer technology in World War II and its rapidly growing power in the second half of this century made it possible to deal with increasingly complex problems, some of which began tu resemble the notion of organized complexity.

## Fuzzy Sets and Fuzzy Logic: Theory and Applications

Initially, it was the common belief of many scientists that the level of complexity we can handle is basically a matter of the level of computational power at our disposal. Later, in the early s, this naive belief was replaced with a more realistic outlook. We began to understand that there are definite limits in dealing with complexity, which neither our human capabilities nor any computer technology can overcome.

One such lirait was determined by Hans Bremermann. The limit is expressed by the proposition; "No data processing system, whether artificial or living, can process more than 2 x bits per second per gram of Is mass.

Using the limit of information, processing obtained for one gram of mass and one second of processing time, Bremermann then calculates the total number of bits processed by a hypothetical computer the size of the Earth within a time period equal to the estimated age of the Earth. Since the mass and age of the Earth are estimated to be less than 6 x grams and 10' years, respectively, and each year contains approximately 3.

The last number-1e—is usually referred to as Bremermann's limit, and problems that require processing more than bits informatio ' u are called iranscomputationai problems. Bremermann's limit seems at first sight rather discouraging, even though it is based on overly optimistic assumptions more reasonable assumptions would result in a number smaller than Indeed, many problems dealing with systems of even modest size exceed the limit in their information-processing demands The nature of these problems has been extensively studied within an area referred to as the theory of computational complexity, which emerged in the s as a branch of the general theory of algorithms.

In spite of the insurmountable computational limits, we continue to pursue the many problems that possess the characteristics of organized complexity. These problems are too - Sec, 1 ,1 Introduction a important for our well being to give up on them. The main challenge in pursuing these problems narrows down fundamentally to one question: how to deal with systems and associated problems whose complexities are beyond our information processing limits?

That is, how can we deal with these problems if no computational power alone is sufficient? In general, we deal with problems in terms of systems that are constructed as models of either some aspects of reality or some desirable man-made objects.

The purpose of constructing models of the former type is to understand some phenomenon of reality, be it natural or man-made, making adequate predictions or retrodictions, learning how to control the phenomenon in any desirable way, and utilizing all these capabilities tor various ends; models of the latter type axe constructed for the purpose of prescribing operations by which a conceived artificial objcet can be constructed in such a way that desirable objective criteria are satisfied within given constraints.

In constructing a model, we always attempt to maximize its usefulness. This aim is closely connected with the relationship among three key characteristics of every systems model: complexity, credibilily, and uncertainly.

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No customer reviews. Share your thoughts with other customers. Write a customer review. There's a problem loading this menu right now. Learn more about site Prime.The primary purpose of the book is to facilitate education in the increasingly important areas of fuzzy set theory and fuzzy logic.

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To ine Fuzzy Sets and Fuzzy Logic is a remarkable achievement; it covers its vast territory with impeccable authority, deep insight and a meticulous attention to detail. We prove only vii and leave vi to the reader. Error rating book.

Although there is enough material in the text for a two-semester course, relevant material may be selected, according to the needs of each individual program, for a one-semester course.