Fuzzy Sets and Fuzzy Logic: Theory and Applications

Book Description

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.

Customer Reviews:

Care is needed.......2006-05-19

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.

First bible of fuzzy systems theory since Dubois and Prade........1998-10-03

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.

Robust treatment of fuzzy logic has interdisciplinary appeal.......1998-09-22

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.

One of the most important book to learn about fuzzy logic.......1998-01-08

The book presents the mathematical theory of fuzzy logic including theorems and demonstrations. There are one part of applications of this logic in many distint areas like engineering, medicine, economics and others.

Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions

Average customer rating:

Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions
Jerry M. Mendel
Manufacturer: Prentice Hall PTR
ProductGroup: Book
Binding: Paperback

General | Computers & Internet | Subjects | Books

General | Software | Computers & Internet | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Computers & Internet | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 0130409693

A First Course in Fuzzy Logic, Third Edition

Average customer rating:

prof. review
A First Course in Fuzzy Logic
Outstanding, for people who are interested in this area

A First Course in Fuzzy Logic, Third Edition
Hung T. Nguyen , and Elbert A. Walker
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

Systems Analysis & Design | Computer Science | Computers & Internet | Subjects | Books

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Computers & Internet | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 1584885262

Book Description

A First Course in Fuzzy Logic, Third Edition continues to provide the ideal introduction to the theory and applications of fuzzy logic. This best-selling text provides a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world applications. New in the Third Edition: · A section on type-2 fuzzy sets - a topic that has received much attention in the past few years · Additional material on copulas and t-norms · More discussions on generalized modus ponens and the compositional rule of inference · Complete revision to the chapter on possibility theory · Significant expansion of the chapter on fuzzy integrals · Many new exercises With its comprehensive updates, this new edition presents all the background necessary for students and professionals to begin using fuzzy logic in its many-and rapidly growing- applications in computer science, mathematics, statistics, and engineering.

Customer Reviews:

prof. review.......2006-01-15

this is the best intro to fuzzy ever writen....im a university prof on the subject of AI so...Ive read tons of books on the subject and this is by far the best intro to fuzzy even for those who ll be learning on their own... very simple put and yet very abording on the matter!

A First Course in Fuzzy Logic.......1999-12-22

If you are looking for a book on Fuzzy Logic Theory, this is a good book. It explains the mathematical basis of fuzzy logic, the mathmatical symbols used, provides proofs for theorems, etc. The chapters and sections are clearly labeled in the table of contents, making it easy to zero in on a topic. It is a College Text Book, with problems to solve at the end of each chapter. Selected problems have answers in the back of the book. Unfortunately, that wasn't the type of book that I expected or needed. I was looking more for the hands on, how to, type of book. That is the only reason it did not get 5 stars.

Outstanding, for people who are interested in this area.......1999-09-21

This is the clearest explanation and application of fuzzy logic that has been published. It is thorough, without being arcane or pedantic.

Introduction to Applied Fuzzy Electronics

Average customer rating:

Introduction to Applied Fuzzy Electronics
Ahmad M. Ibrahim
Manufacturer: Prentice Hall
ProductGroup: Book
Binding: Hardcover

General | Reference | Subjects | Books

General | Arts & Photography | Subjects | Books

Applied | Physics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Arts & Photography | Qualifying Textbooks - Fall 2007 | Stores | Books

Computers & Internet | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Reference | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 0132064006

Book Description

KEY BENEFIT: This book provides a self-contained, compact introduction to fuzzy logic from an applied electronics point of view. It presents fuzzy electronics as a generalization of digital electronics with the goal of making fuzzy logic easily accessible to practicing engineers and students alike.

Advanced Engineering Mathematics with MATLAB (Bookware Companion)

Average customer rating:

Excellent book, but missing import parts for Electronics/Com
Deserves 6 stars
Excellent reference for engineers

Advanced Engineering Mathematics with MATLAB (Bookware Companion)
Thomas L. Harman , James B. Dabney , and Norman John Richert
Manufacturer: Cengage-Engineering
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

Electrical & Electronics | Engineering | New & Used Textbooks | Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Computers & Internet | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 0534371647

Book Description

ADVANCED ENGINEERING MATHEMATICS WITH MATLAB® is written for engineers and engineering students who are interested in applying MATLAB® to solve practical engineering problems. The book emphasizes mathematical principles, not computations, with MATLAB® employed as a tool for analysis that shows how engineering problems are defined and solved. The book features complete MATLAB® integration throughout, abundant examples which show real practical applications, and end-of-chapter problems that reinforce techniques.

Customer Reviews:

Excellent book, but missing import parts for Electronics/Com.......2002-05-27

This is an excellent book for studying advanced math. Important concepts clearly explained with good matlab examples. But I was surprised to find this book titled "Engineering Math" with the miss out of some thing like probability and random variables which are of the critical importance for Electronics/Communications students.

Deserves 6 stars.......2001-07-05

If you are not already a superuser of MATLAB or a mathematician and want to choose one single book on MATLAB that also brings a solid math base, this is the one. The authors have chosen the subjects very well, with emphasys on the use of mathematical principles coupled with the use of the computing power offered by MATLAB.

In addition to a sound presentation of concepts - without however being extensive (or boring) on theoretical details that probably would not be relevant - this book addresses most areas of University Math (Physical Sciences undergraduate curriculum) with a wealth of good practical programming examples. I specially liked the chapters on Eigenvectors and Eigenvalues, those on Differential equations, Fourier analysis and the simple but very clear and didatic one on Discrete sytems.

In summary, although not a complete text, the subjects addressed in this book are so well presented that it can be forgiven for not covering some areas (like complex variables and calculus of variations, to name only two). There is no waste of pages in this book, but as a suggestion for future enhancement I would mention the inclusion of a chapter dedicated to exploring the graphing power available in MATLAB.

Also as a reference, for most needs you'll probably be able to start doing something productive right away after reading. Well worth its price!

Excellent reference for engineers.......2000-08-07

This is an excellent reference book not only for matlab, also an excellent reference book for the basic concepts such as Fourier Analysis. I think any engineers who work in electric design filed must have a copy.

Uncertainty-Based Information: Elements of Generalized Information Theory (Studies in Fuzziness and Soft Computing)

Average customer rating:

Never by this book
Interesting and Valuable

Uncertainty-Based Information: Elements of Generalized Information Theory (Studies in Fuzziness and Soft Computing)
George J. Klir , and Mark J. Wierman
Manufacturer: Physica-Verlag Heidelberg
ProductGroup: Book
Binding: Hardcover

Information Theory | Computer Science | Computers & Internet | Subjects | Books

General | Computers & Internet | Subjects | Books

Chaos & Systems | Physics | Science | Subjects | Books

General | Science | Subjects | Books

General | Medicine | Subjects | Books

All Amazon Upgrade | Amazon Upgrade | Stores | Books

Computers & Internet | Amazon Upgrade | Stores | Books

Medicine | Amazon Upgrade | Stores | Books

Professional & Technical | Amazon Upgrade | Stores | Books

Science | Amazon Upgrade | Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 3790812420

Book Description

The book is an overview of the development of basic ideas and mathematical results regarding measures and principles of uncertainty-based information formalized within the framework of classical set theory, probability theory, fuzzy set theory, possibility theory, and the Dempster-Shafer theory of evidence.
The book contains many new results, which had until now not been available in a single monograph. The book is very useful for researchers, but it can also be used as a graduate text.

Customer Reviews:

Never by this book.......2006-02-05

This book is trash, I will never, ever suggest anyone
buying this book! Save your money for the other books.

Interesting and Valuable.......1999-03-12

a great book for fuzzy field

Fuzzy Mathematical Models in Engineering and Management Science

Average customer rating:

Fuzzy Mathematical Models in Engineering and Management Science
Arnold Kaufmann
Manufacturer: North-Holland
ProductGroup: Book
Binding: Hardcover

Operations Research | Management & Leadership | Business & Investing | Subjects | Books

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Adaptive Modelling, Estimation and Fusion from Data

Average customer rating:

Where is the data ?

Adaptive Modelling, Estimation and Fusion from Data
Chris Harris , Xia Hong , and Qiang Gan
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

General | Computers & Internet | Subjects | Books

General | Software | Computers & Internet | Subjects | Books

All Amazon Upgrade | Amazon Upgrade | Stores | Books

Computers & Internet | Amazon Upgrade | Stores | Books

Professional & Technical | Amazon Upgrade | Stores | Books

Science | Amazon Upgrade | Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Computers & Internet | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 3540426868

Book Description

In a world of almost permanent and rapidly increasing electronic data availability, techniques of filtering, compressing, and interpreting this data to transform it into valuable and easily comprehensible information is of utmost importance. One key topic in this area is the capability to deduce future system behavior from a given data input.

This book brings together for the first time the complete theory of data-based neurofuzzy modelling and the linguistic attributes of fuzzy logic in a single cohesive mathematical framework. After introducing the basic theory of data-based modelling, new concepts including extended additive and multiplicative submodels are developed and their extensions to state estimation and data fusion are derived. All these algorithms are illustrated with benchmark and real-life examples to demonstrate their efficiency.

Chris Harris and his group have carried out pioneering work which has tied together the fields of neural networks and linguistic rule-based algortihms. This book is aimed at researchers and scientists in time series modeling, empirical data modeling, knowledge discovery, data mining, and data fusion.

Customer Reviews:

Where is the data ?.......2003-05-26

While i do not deny the contribution at providing a more or less complete treatment of neurofuzzy techniques for data modeling, i'm still wondering where the non-theoretical chapters dealing with how to cope with real data with these techniques are hidden. The few examples in the book are mostly artificial and very limited in their scope. i'm not sure people dealing with data have an interest at reading this book, it's more about neurofuzzy techniques than data modelling.

The book edited by Schwefel, Weneger and Weinert entitled "Advances in computational intelligence" published by Springer emphasizes a lot more on fuzzy techniques based on real data although it does not discuss the "neuro" part of "neuro-fuzzy" techniques.

Book Description

In this innovative approach to the practice of social science, Charles Ragin explores the use of fuzzy sets to bridge the divide between quantitative and qualitative methods. Paradoxically, the fuzzy set is a powerful tool because it replaces an unwieldy, "fuzzy" instrument—the variable, which establishes only the positions of cases relative to each other, with a precise one—degree of membership in a well-defined set.

Ragin argues that fuzzy sets allow a far richer dialogue between ideas and evidence in social research than previously possible. They let quantitative researchers abandon "homogenizing assumptions" about cases and causes, they extend diversity-oriented research strategies, and they provide a powerful connection between theory and data analysis. Most important, fuzzy sets can be carefully tailored to fit evolving theoretical concepts, sharpening quantitative tools with in-depth knowledge gained through qualitative, case-oriented inquiry. This book will revolutionize research methods not only in sociology, political science, and anthropology but in any field of inquiry dealing with complex patterns of causation.

Customer Reviews:

This book is a great first step in reorienting social science.......2007-07-13

Where to start? Well, first the second reviewer is off the mark with the critique about the specificity regarding the IMF. This is not a book about the IMF, so the lack of exhaustive it not a fatal flaw. What this book attempt to accomplish is to get one to think about new ways of categorizing social phenomena. Too much of quantitative method assumes that one can make clear distinctions between categories. This is stating the case much too strongly to reflect reality in an acceptable manner. What Ragin does is offer some theorizing about how one can recognize the fuzzy-boundaries of social phenomena. His insight rests on the use of key characteristics to provide the metric for those who will try to better reflect social events in their research. If you wish to create a better explanation of what you are studying then purchase this book. It is sure to improve your research and how you theorize about the objects you study.

Fuzzy subjectivity.......2005-05-05

I find crisp sets problematic. Hoping to resolve some of the problems (for qualitative and comparative research) of crisp sets, I turned to this text. Ragin repeats himself time and time again in this text. Some complex topics (concentration, dilation, complex theoretical statements) receive minimal attention, leaving readers out in the cold. He fails to establish the efficacy of fuzzy sets for sufficiency or necessity. Ragin also fails to support why necessity is either valuable or possible in social sciences. I would seek to argue that necessity is virtually impossible to determine in social sciences. J.S. Mill was no sociologist. Also, when Ragin attempts to illustrate the application of fuzzy-set methods to IMF protests (chapter 10), he seems to neglect to include certain steps in the calculation of membership scores in the set with severe IMF protests. Ragin does not provide enough qualitative data to support why each country was indicated to have membership in his seven levels of IMF protest membership (p. 265). Also, when Ragin discusses assessment of fuzzy set membership (p. 165 - 171), I feel that fuzzy set membership assignment provides too much flexibility to individual researchers that severely hampers retestability (or even critical analysis) of the data. Ragin skirts the issue of researcher subjectivity when he makes statements like (p. 166, and similar statements in other portions of the text): "The steps I sketch here assume that researchers have a solid understanding of the concepts appearing in their theories and that they have an extensive base of relevant substantive knowledge as well." I certainly feel that the 'crisp-set approach' can be highly problematic, but Ragin's fuzzy-set approach does not seem to be a well-formulated answer to social scientific quandrys presented by crisp sets.

useful place to start but by no means the final story.......2001-10-25

There are two aspects to Ragin's book. The first part of the book is really an update of his general methodological program first set forth in The Comparative Method. It does add some new things to the older material and is thus worth the look. Ragin has some important points to make and deserves to be paid careful attention by social scientists of both qualitative and quantitative traditions.

The second part is a relatively gentle--too gentle in my view--introduction to fuzzy set theory as well as to some applications to social scientific problems that can be addressed with FST. This is useful since it won't put readers off with lots of heavy math they're unlikely to understand. However, the presentation of FST in this book is weak. IMO the worst deficiency is that it lacks cites to more detailed literature that would be necessary for anyone who wanted to apply FST to real problems.

Customer Reviews:

From an Industrial Practitioner of Process Measurement & Control.......2006-07-10

An excellent option if you are looking for business and industry examples and applications of Fuzzy Logic.

If you are looking for more in-depth knowledge and theory about Fuzzy Logic you should consider "The Fuzzy Systems Handbook: A Practitioner's Guide to Building, Using, & Maintaining Fuzzy Systems" by the same author.

Hands on fuzzy logic book.......2001-07-19

This book compliments The Fuzzy Systems Handbook very well. (BTW, The Fuzzy Systems Handbook, also by Earl Cox, is one of the most usable Fuzzy Logic books that I have on my bookshelf) The practical examples in Fuzzy Logic for Business and Industry, provide users with tools to implement Fuzzy Logic in real world applications. If you want a book explaining Fuzzy Logic principles, this is not the book for you. If you want to get insight into the application of Fuzzy Logic in business scenarios, this is a very worthwhile starting point.

Not as good as the Fuzzy Logic Handbook.......2001-06-26

In this book the concepts of Fuzzy Logic are outlined reasonably well, but emphasis is put on the so called 'applicability' of fuzzy reasoning in business applications. By working through several business examples in depth, a fair coverage of the topic is provided. The step by step description of the fuzzy process is a bonus towards understanding how the model arrives at it's end results.

However, compared with the Fuzzy Logic Handbook, this book relies too heavily on the examples. It lacks the clear description of some of the underlying mathematics and their relevance provided in the Handbook aswell as a solid foundation of the principles of fuzzy logic.

On the other hand, this book provides long and detailed examples that can be usefull in combination with the sometimes short descriptions provided in the Handbook.

If you are looking for a good introduction into Fuzzy Logic, this is not the right book, if however you are somewhat familiar with the principles and want to see for yourself how fuzzy logic works, this book provides some nicely worked out examples.

Books:

Books Index

Books Home

Recommended Books