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

Jerry M. Mendel (Author)

Book Description

ISBN-10: 0130409693 | ISBN-13: 978-0130409690 | Publication Date: January 1, 2001 | Edition: 1

For courses in Neural Networks and Fuzzy Systems; Fuzzy Systems/Control; Fuzzy Logic. The first book of its kind, this text explains how all kinds of uncertainties can be handled within the framework of a common theory and set of design tools--fuzzy logic systems--by moving the original fuzzy logic to the next level--type-2 fuzzy logic. It presents a complete development of both type-1 and type-2 fuzzy logic systems, showing how the expanded and richer fuzzy logic contains the original fuzzy logic within it. The text demonstrates, beyond a reasonable doubt, that when uncertainties are present in a problem, much better performance is obtained by using a type-2 fuzzy logic system than by using a type-1 fuzzy logic system.

Editorial Reviews

From the Inside Flap

Preface

Uncertainty is the fabric that makes life interesting. For millenia human beings have developed strategies to cope with a plethora of uncertainties, never absolutely sure what the consequences would be, but hopeful that the deleterious effects of those uncertainties could be minimized. This book presents a complete methodology for accomplishing this within the framework of fuzzy logic (FL). This is not the original FL, but is an expanded and richer FL, one that contains the original FL within it.

The original FL, founded by Lotfi Zadeh, has been around for more than 35 years, as of the year 2000, and yet it is unable to handle uncertainties. By handle, I mean to model and minimize the effect of. That the original FL—type-1 FL—cannot do this sounds paradoxical because the word fuzzy has the connotation of uncertainty. The expanded FL—type-2 FL—is able to handle uncertainties because it can model them and minimize their effects. And, if all uncertainties disappear, type-2 FL reduces to type-1 FL, in much the same way that if randomness disappears, probability reduces to determinism.

Although many applications were found for type-1 FL, it is its application to rule-based systems that has most significantly demonstrated its importance as a powerful design methodology. Such rule-based fuzzy logic systems (FLSs), both type-1 and type-2, are what this book is about. In it I show how to use FL in new ways and how to effectively solve problems that are awash in uncertainties.

FL has already been applied in numerous fields, in many of which uncertainties are present (e.g., signal processing, digital communications, computer and communication networks, diagnostic medicine, operations research, financial investing, control, etc.). Hence, the results in this book can immediately be used in all of these fields. To demonstrate the performance advantages for type-2 FLSs over their type-1 counterparts, when uncertainties are present, I describe and provide results for the following applications in this book: forecasting of time series, knowledge-mining using surveys, classification of video data working directly with compressed data, equalization of time-varying nonlinear digital communication channels, overcoming co-channel interference and intersymbol interference for time-varying nonlinear digital communication channels, and connection admission control for asynchronous transfer mode networks. No control applications have been included, because to date type-2 FL has not yet been applied to them; hence, this book is not about FL control, although its methodologies may someday be applicable to it.

I have organized this book into four parts. Part 1— Preliminaries — contains four chapters that provide background materials about uncertainty, membership functions, and two case studies (forecasting of time-series and knowledge mining using surveys) that are carried throughout the book. Part 2—Type-1 Fuzzy Logic Systems—contains two chapters that are included to provide the underlying basis for the new type-2 FLSs, so that we can compare type-2 results for our case studies with type-1 results. Part 3—Type-2 Fuzzy Sets—contains three chapters, each of which focuses on a different aspect of such sets. Part 4—Type-2 Fuzzy Logic Systems—which is the heart of the book, contains five chapters, four having to do with different architectures for a FLS and how to handle different kinds of uncertainties within them, and one having to do primarily with four specific applications of type-2 FLSs.

This book can be read by anyone who has an undergraduate BS degree and should be of great interest to computer scientists and engineers who already use or want to use rule-based systems and are concerned with how to handle uncertainties about such systems. I have included many worked-out examples in the text, and have also included homework problems at the end of most chapters so that the book can be used in a classroom setting as well as a technical reference.

Here are some specific ways that this book can be used:

For the person totally unfamiliar with FL who wants a quick introduction to it, read the Supplement to Chapter 1 and Chapter 5 (Sections 5.1-5.8).

For the person who wants an in-depth treatment of type-1 rule-based FLSs, read the Supplement to Chapter 1 and Chapters 4-6.

For the person who is only interested in type-2 fuzzy set theory, read Chapters 3, 7-9, and Appendices A and B.

For a person who wants to give a course on rule-based fuzzy logic systems, use Chapters 1-12 and 13 (if time permits). Chapter 14 should be of interest to people with a background in digital communications, pattern recognition, or communication networks and will suggest projects for a course.

For a person who is a proponent of Takagi-Sugeno-Kang (TSK) fuzzy systems and wants to see what their type-2 counterparts look like, read Chapters 3, 7-9, and 13.

For a person who is interested in forecasting of time-series and wants to get a quick overview of the benefits to modeling uncertainties on forecasting performance when using rule-based forecasters, read Chapters 4 (Section 4.2), 5 (Section 5.10), 6 (Section 6.7), 10 (Section 10.11), 11 (Section 11.5), and 12 (Section 12.5).

For a person who is interested in knowledge mining and wants to get a quick overview of the benefits to modeling uncertainties on judgment making when using rule-based advisors, read Chapters 4 (Section 4.3), 5 (Section 5.11), and 10 (Section 10.12).

So that people will start using type-2 FL as soon as possible, I have made free software available online for implementing and designing type-1 and type-2 FLSs. It is MATLAB-based (MATLAB is a registered trademark of The MathWorks, Inc.A computation section, which directs the reader to very specific M-files, appears at the end of most chapters of this book. Appendix C summarizes all of the M-files so that the reader can see the forest from the trees.

From the Back Cover

• Type-2 fuzzy logic: Breakthrough techniques for modeling uncertainty
• Key applications: digital mobile communications, computer networking, and video traffic classification
• Detailed case studies: Forecasting time series and knowledge mining
• Contains 90+ worked examples, 110+ figures, and brief introductory primers on fuzzy logic and fuzzy sets

Breakthrough fuzzy logic techniques for handling real-world uncertainty.

The world is full of uncertainty that classical fuzzy logic can't model. Now, however, there's an approach to fuzzy logic that can model uncertainty: "type-2" fuzzy logic. In this book, the developer of type-2 fuzzy logic demonstrates how it overcomes the limitations of classical fuzzy logic, enabling a wide range of applications from digital mobile communications to knowledge mining. Dr. Jerry Mendel presents a bottom-up approach that begins by introducing traditional "type-1" fuzzy logic, explains how it can be modified to handle uncertainty, and, finally, adds layers of complexity to handle increasingly sophisticated applications. Coverage includes:

• The sources of uncertainty and the role of membership functions
• Type-2 fuzzy sets: operations, properties, and centroids
• Singleton, non-singleton, and TSK Type 2 fuzzy logic systems
• Comparing "type-2" and "type 1" results
• Extensive applications coverage: digital mobile communications, computer networking, and video traffic classification
• Two start-to-finish case studies: Forecasting time series and knowledge mining

Carefully balanced between theory and design, the book contains over 90 worked examples and more than 110 figures. It is ideal for engineers, scientists, computer science researchers, and mathematicians interested in AI, rule-based systems, and modeling uncertainty. Since it contains brief introductory primers on fuzzy logic and fuzzy sets, it's accessible to virtually anyone with an undergraduate B.S. degree—including computing professionals designing and implementing rule-based systems.

SOFTWARE RESOURCES

Online software includes more than 30 companion MATLAB m-files for implementing a wide variety of type-1 and type-2 fuzzy logic systems.

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Product Details

• Paperback: 576 pages
• Publisher: Prentice Hall; 1 edition (January 1, 2001)
• Language: English
• ISBN-10: 0130409693
• ISBN-13: 978-0130409690
• Product Dimensions: 9.2 x 7 x 1.2 inches
• Shipping Weight: 2.1 pounds (View shipping rates and policies)
• Average Customer Review: 2.8 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #1,457,294 in Books (See Top 100 in Books)

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2 of 2 people found the following review helpful:

5.0 out of 5 stars A must book for superior understanding of general fuzzy systems, April 20, 2008

By 

H. Malik "Kashmiri" (Australia) - See all my reviews
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This review is from: Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions (Paperback)

This is an absolutely brilliant work focusing on both fundamental aspects of Fuzzy logic systems. Firstly an intuitive and physical understanding essential for diverse applications of fuzzy sets is developed while at the same time mathematically sound treatment of fundamentals is carried out. There is no other book which integrates clarity and the underlying mathematics to such high level. The treatment of type-2 fuzzy sets is unrivalled by all standards. Mendel is perhaps first time ever in a published book, gives a truly geometric and easy to understand description of type-2 fuzzy sets, making lives of PhD students like myself easier. However, book can be read and used for applications by any one with undergraduate degree in science, engineering or even finance etc and requires moderate mathematical maturity. All relevant mathematical aspects of fuzzy logic systems are covered in detailed in the book itself.

The book begins with a comprehensive and deep treatment of type-1 logic system or in other words, ordinary fuzzy set theory. Then type-2 fuzzy is introduced early on with extremely easy to understand format. While theory of ordinary fuzzy logic is developed to the full extend in part 1, part two of the book, focuses on parallel development of type-2 fuzzy sets. There are no other works, except perhaps Mendel's own published papers, which have such easy to understand and easy to internalized treatment of relatively new and difficult area of type-2 fuzzy logic system. Throughout the easy to understand examples with detail applications of type-2 fuzzy logic system to engineering ranging from digital communications to knowledge mining are given.

While mathematical aspects are covered in detail and without sacrificing required rigor, overall style is quite informal and very easy to read. The book successfully advocates the use of type-2 fuzzy logic systems as a generalization of type-1 fuzzy logic system while demonstrating increased applicable power of type-2 fuzzy systems to tackle difficult engineering and scientific problems including but not limited to time varying, systems, systems involving non-stationary noise processes and nonlinear systems.

Relevant examples of above areas are considered in detail along with reasons to use type-2 fuzzy systems as a solution mechanism. Examples of application areas covered include equalizations of nonlinear and time-varying digital communications channels, rule based classifications of video traffic, knowledge mining using IF-THEN questionnaires and so on. This aspect makes this book quite unique and allows easier transition from described theory to the required applications for the reader.

In the final analysis, this is the perhaps the only book available, which while stressing mathematical details relating to type-1 and type-2 fuzzy logic systems, provides physical and intuitive understanding drawn from detailed discussions and heavily supplemented with figures and pictures with remarkable clarity as well as gives easier to follow practical application based examples. All three aspects work together in a synergetic manner to clarify and imprint deep knowledge relating to fuzzy systems in the minds of the readers.

Last but not least, detailed computer programs in Matlab are provided covering both type-1 and type-2 fuzzy logic systems. This aspect allows immediate applications to practical problems.

This book is greatly appreciated and highly recommended for anyone interested in type-1, or type-2 fuzzy logic systems aiming either to deeply understand these important areas or to apply them in his or her field of interest.

4.0 out of 5 stars The Best Book, November 23, 2009

By 

Vitor E. Andrade "VitorE" (Salvador, Brazil) - See all my reviews
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This review is from: Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions (Paperback)

It's all that you need to learn about Fuzzy Sets and Systems. Even because Jerry Mendel is one of the most important researchers of Fuzzy. The only problem is that the book hasn't a good finishing.

0 of 3 people found the following review helpful:

1.0 out of 5 stars Don't waste your money, February 5, 2010

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A reader "A reader" - See all my reviews

This review is from: Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions (Paperback)

The subject matter is fascinating, but this paperback book arrived with the binding already broken. I've had the book less than a week and about 40 pages have already fallen out. Prentice-Hall used to be a reputable company, but evidently no more.