Fuzzy Sets and Fuzzy Logic: Theory and Applications [Paperback]

George J. Klir (Author), Bo Yuan (Author)

Book Description

Publication Date: May 21, 1995 | ISBN-10: 0131011715 | ISBN-13: 978-0131011717 | Edition: 1st

Reflecting the tremendous advances that have taken place in the study of fuzzy set theory and fuzzy logic from 1988 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. Theoretical aspects of fuzzy set theory and fuzzy logic are covered in Part I of the text, including: basic types of fuzzy sets; connections between fuzzy sets and crisp sets; the various aggregation operations of fuzzy sets; fuzzy numbers and arithmetic operations on fuzzy numbers; fuzzy relations and the study of fuzzy relation equations. Part II is devoted to applications of fuzzy set theory and fuzzy logic, including: various methods for constructing membership functions of fuzzy sets; the use of fuzzy logic for approximate reasoning in expert systems; fuzzy systems and controllers; fuzzy databases; fuzzy decision making; and engineering applications. For everyone interested in an introduction to fuzzy set theory and fuzzy logic.

Editorial Reviews

From the Publisher

Reflecting the tremendous advances that have taken place in the study of fuzzy set theory and fuzzy logic from 1988 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.

From the Back Cover

Reflecting the tremendous advances that have taken place in the study of fuzzy set theory and fuzzy logic from 1988 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. Theoretical aspects of fuzzy set theory and fuzzy logic are covered in Part I of the text, including: basic types of fuzzy sets; connections between fuzzy sets and crisp sets; the various aggregation operations of fuzzy sets; fuzzy numbers and arithmetic operations on fuzzy numbers; fuzzy relations and the study of fuzzy relation equations. Part II is devoted to applications of fuzzy set theory and fuzzy logic, including: various methods for constructing membership functions of fuzzy sets; the use of fuzzy logic for approximate reasoning in expert systems; fuzzy systems and controllers; fuzzy databases; fuzzy decision making; and engineering applications. For everyone interested in an introduction to fuzzy set theory and fuzzy logic.

See all Editorial Reviews

Product Details

• Paperback: 592 pages
• Publisher: Prentice Hall; 1st edition (May 21, 1995)
• Language: English
• ISBN-10: 0131011715
• ISBN-13: 978-0131011717
• Product Dimensions: 9.3 x 7.3 x 1.2 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #240,506 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

22 of 22 people found the following review helpful:

4.0 out of 5 stars First bible of fuzzy systems theory since Dubois and Prade., October 2, 1998

By 

DR SILER "William Siler" (Alabama, USA) - See all my reviews
(REAL NAME)   

This review is from: Fuzzy Sets and Fuzzy Logic: Theory and Applications (Paperback)

A comprehensive and authoritative presentation of developments in the mathematics of fuzzy systems theory over the past thiry years. While the basic mathematics are presented, this book is not for the casual reader, but for those seriously interested in fuzzy systems theory. If the reader does not have a good mathematical background, he or she will find this book tough going. Coverage of theoretical fuzzy concepts is quite complete, including theory of fuzzy sets, fuzzy arithmetic, fuzzy relations, possiblity theory, fuzzy logic and uncertainty-based information.

The applications section presents theory which could be useful in applications rather than the applications themselves. References are given, but no distinction is made between theoretical work and real-world applications, and many of the references are old and out-of-date.

For a reference book on fuzzy mathematics, this book is superb; as a pointer to real-world applications, it leaves something to be desired.

20 of 20 people found the following review helpful:

5.0 out of 5 stars Robust treatment of fuzzy logic has interdisciplinary appeal, September 21, 1998

By 

Dr. Kasumu O. Salawu (Maplewood, New Jersey USA) - See all my reviews
(REAL NAME)   

This review is from: Fuzzy Sets and Fuzzy Logic: Theory and Applications (Paperback)

George and Bo have been as thorough and lucid in preparing this book as well as George explicated systems thinking in the very first book of his I read, "An Approach to General Systems Theory." Here, as there, without compromising mathematical rigor, the goal of this book is to elaborate its subject matter in such a robust manner that it has multidisciplinary appeal. As always, the reader is given a flexible, almost interactive, access to the what, why and how of fuzzy thinking. Despite the exception taken by Professor Lotfi A. Zadeh, the "founder of fuzzy logic," the percipient reader will appreciate the authors' unusual association of "fuzzy measure," that is, the degree of belief that a particular element belongs to a crisp set, (not the degree of membership in the set), with Possibility Theory so as to clarify the differences between fuzzy set theory and probability theory. The illustrative applications are not only case studies that one may pick and choose from for examination and emulation but also constitute incontrovertible evidence of the successful and promising realization of the fuzzy paradigm. As a former professor of engineering at Rutgers University, I found the 79-page Instructor's manual helpful for self- or extended study and I assume it would be valuable for teaching. I have read many books on fuzzy logic and I judge this to be the most balanced to date, (early 1998), - not filled with C++ code or trying to sell a software package nor is it theoretically daunting - it is simply an inviting demonstration of how fuzzy logic clears up foggy modeling and analysis.

10 of 10 people found the following review helpful:

5.0 out of 5 stars Care is needed, May 18, 2006

By 

Douglas A. Lefelhocz (Macedonia, Ohio) - See all my reviews
(REAL NAME)   

This review is from: Fuzzy Sets and Fuzzy Logic: Theory and Applications (Paperback)

I would hesistate to give anything less than a 5 star review to anything on fuzzy set theory in the wide sense. Make no mistake reading this book is worth your time. Yet, some significant problems do exist with this text.

First off, read the proofs in this carefully and figure out if they do work. Klir and Yuan know that appealing to contradiction in theorem proving doesn't often work out in fuzzy theory. Yet, they go ahead and use it almost recklessly. One example is their proof on fuzzy numbers that says that they are all continuous on pages 99 to 100. After about a full, condensed page of mathematical reasoning they say that left fuzzy numbers are continuous from the left and that right fuzzy numbers are continuous from the right. After their supposed "proof" they claim that "The implication of Theorem 4.1 is that every fuzzy number be represented in the form of (4.1)." 4.1 shows a discontinuous fuzzy number. A jump discontinuity to speak more specifically. Consequently, their supposed "theorem" doesn't exactly work as a "theorem". Perhaps I misunderstand and they have some different idea of continuity. I don't get it though and neither does any other mathematician, as any break in a function whatsoever means discontinuity.

More interestingly, some of their axioms for fuzzy set don't hold. For instance, on page 62 Axiom i1 (i for intersection) says that i(a, 1)=a, which they label as the "boundary conidition." This does hold for drastic products. However, it doesn't hold for all fuzzy intersections. As Buckley and Eslami point out the axioms or necessary conditions for fuzzy intersections work out as "(1) 0<=a, b<=1 and i(a, b) is in

[0, 1]; (2) i(1, 1)=1; and (3) i(0, 1)=i(1, 0)=i(0, 0)=0." Consquently, (ab)/max{a, b, .5} qualifies as a fuzzy intersections. Here i(.6, .4)=.24/.6=24/60=2/5=.4

I don't exactly mean the above to significantly downgrade the work of Klir and Yuan. Their collection of papers of Zadeh does have signficant value, even if it costs a lot. The sheer enormity and very comprehensive nature of this quasi-encyclopedia makes it worth the read. The problems are interesting and challenging, if you choose to do them. I do appreciate the authors mentioning that the problems are meant to enchance the reader's understanding. That Klir and Yuan provide a comprehensive bibliography and consulted many, many original papers before and while writing their text alone indicates they do know something and did some thinking here. Their graphs do help to illustrate their ideas. So, I do advise that you read the book. Just read carefully.