Fuzzy-Logic Books

Buckley and Eslami's notation and some of their ideas on fuzzy sets might go deeper than many others. I've found this book intriguing to say the least. You'll find this a very concise "no-nonsense" sort of math book. Ideas get explained in a few sentences or in a few paragraphs, and then come the exercises! And you'll find even more new ideas, not mentioned in the reading, in the exercises. I do like this sort of style of learning mathematics, because it actively gets you involved.
This book and others on fuzzy set theories do require a decent understaning of crisp set theory. So, if one hasn't taken a course or read a book on crisp set theory you might want to check out a copy of Seymour Lipschutz's Schaum's Outline "Theory and Problems of Set Theory." Knowing some basic calculus will also help. Some advantages of this book lie in that it helps one to separate the idea of fuzzy intersections and fuzzy unions from the standard and useful idea of t-norms and t-conorms. Sections on fuzzy geometry, fuzzy trignometry also seem interesting as these ideas have not yet gotten much development.
I think I've detected a potential error in the text in that it gives an integral for an equation that had to have had part of the integral as negative. But, this seems relatively minor. The book could easily get improved if the author(s) provided solved examples of their exercises, or at least answers. Something like a Schaum's Outline of Fuzzy Set Theory would be an excellent idea!
I appreciate simple things in this text like the authors not saying "prove this truth table..." and instead saying "prove or disprove...", and not saying "prove" in general, but rather saying "show".

Fuzzy sets and fuzzy logic are knowledge representation systems where the values assigned to the variables are selected from a range, generally from 0.0 to 1.0. With 0.0 representing not possible or false and 1.0 representing certainty or true, this provides a more reasonable way to represent values in the real world. Classical logic is restricted to variables restricted to the true/false binary selection and there is a complete set of rules to create inference and decision systems in classical logic. Clearly, fuzzy logic restricted to the extreme values defaults to classical logic.
There are fuzzy analogs to the inference structures in classical logic and they are explained in the first three papers in this book. The introductory material is complete, although it will be difficult to understand if you have no background in logic. The remaining thirteen papers deal with specific applications of fuzzy logic and reasoning to real-world problems. The papers are:

*) Fuzzy logic controllers
*) Methods and applications of fuzzy mathematical programming
*) Fuzzy set methods in computer vision
*) Fuzziness, image information and scene analysis
*) Fuzzy sets in natural language processing
*) Fuzzy-set-theoretic applications in modeling of man-machine interactions
*) Questionnaires and fuzziness
*) Fuzzy logic knowledge systems and artificial neural networks in medicine and biology
*) The representation and use of uncertainty and metaknowledge in Milord
*) Fuzzy logic with linguistic quantifiers in group decision making
*) Learning in uncertain environments
*) Evidential reasoning under probabilistic and fuzzy uncertainties
*) Probabilistic sets-probabilistic extensions of fuzzy sets

As you can see from the titles of the papers, the applications to which fuzzy operations can be applied are of considerable breadth.
If you are interested in the fundamentals of fuzzy reasoning and how it can be applied, then this is a book that you will find of great interest. Most of the papers are very technical in nature, so some background in the specific field is necessary if you are to have a complete understanding of the operations.

This is the best book on fuzzy logic that I have ever seen. Hajek and Medvedev present the latest results up to 1996 including the remarkable comparison of fuzzy logic with probability and logic. I have recently extended his results by proving that logic-based probability (LBP) given by P(A-->B) = 1 - P(A) + P(AB) where AB is the intersection or conjunction of A and B is more general than modal logic FP(RPL with product conjunction) because the conditional probability P(B/A) is related to P(A-->B) by P(A-->B) - 1 + P(A) = P(AB) = P(B/A)P(A) and replacing P(AB) and P(B/A) everywhere by P(A-->B) yields a more general logic because P(A-->B) is defined even when P(A) is 0, unlike P(B/A). I especially recommend chapter 8, Generalized Quantifiers and Modalities, which discuss crisp and fuzzy "probably" and "many" , chapter 3 which discusses Lukaciewicz propositional logic (which is closely related to LBP)and Rational Pavelka Logic (RPL) which is an extension of Lukaciewicz's logic. Chapter 1 is important for preliminaries and chapter 2 covers many-valued logics. The reader not well versed in logic and mathematics should hire a reputable consultant or tutor to translate the book into mostly ordinary English (which can be done, at the loss of some rigor). This is because fuzzy logic is entering into everything nowadays, from computers to robots to engineering and social sciences. Multivalued logics, which were for so long criticized (together with fuzzy logics) by critics except some at the University of Vienna and similar places, turn out to have important applications and properties. (I must admit that when I was working for the CSE (Center for the Study of Evaluation) at UCLA in the 1970s, I recommended against researching fuzzy logic, which was one of my worst decisions. I thought that it was insufficiently rigorous in terms of information/knowledge.)

I have never read about Neuro-Fuzzy Pattern Recognition and I was very glad to see this book's first chapter explain, in detail, the theory behind the subject and give good examples.
What really makes this book great is that it doesn't rely just on theory and math, but provides actual implimentable examples by giving an example (the ones explaining finger prints are great), showing you various problems you will have, and how to get around them.

If you want to code a program that uses fuzzy pattern recog this book will be your guide as it takes you from 0 to 100 and never lets you down.

This is a good book, but my immediate need is for a much more introductory book. I'm just through the first chapter and have already encountered ideas and concepts I've never heard before, and my undergraduate major was mathematics! What's the textbook(s) for the prerequisite(s) for the class that would use "Principles..."?

This is not your usual everyday story: oh, no! It goes even further than that and its implications are far more outreaching. Interested? Read on...

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.

these books just crack me up, my only complaint is they are too short! I never want to put them down, and read the whole thing in one sitting.

What is so amazing to me is that Get Fuzzy has from the very beginning been extremely funny and the characters fully conceived. The level of excellence and humor is always in place. One can't go wrong getting a Fuzzy book. A great present for the entire household and important for those who collect Get Fuzzy and want to be able to return to Fuzzy world just by opening a book.

I won't go into how fantastic this comic strip is, but it is easily my favorite comic strip of all time. :)

For the uninitiated, there are eight collections so far and three treasuries. The fourth treasury is not yet released.

Please keep in mind that each treasury is two collections put together, so as far as I know the treasuries are the same as two of the collections, except I believe the treasuries have the Sunday comics in color while the collections have them in black and white.

In chronological order, the collections are:

1. The Dog is Not a Toy: House Rule #4
2. Fuzzy Logic: Get Fuzzy 2
3. The Get Fuzzy Experience
4. Blueprint for Disaster
5. Say Cheesy: A Get Fuzzy Collection 5
6. Scrum Bums
7. I'm Ready for My Movie Contract: A Get Fuzzy Collection
8. Take Our Cat, Please: A Get Fuzzy Collection

The treasuries are:

1. Groovitude (encompassing collections 1 and 2).
2. Bucky Katt's Big Book of Fun (encompassing collections 3 and 4).
3. Loserpalooza (encompassing collections 5 and 6).
4. The Potpourrific Great Big Grab Bag of Get Fuzzy (encompassing collections 7 and 8). (not yet released - release date is currently 9/1/08)

These comics are beyond hilarious, and I would highly recommend them to pet lovers/haters of all ages. :)

What can I say, I'm a sucker for Bucky and Sachel. This book is a compilation of past strips that are wonderfully hilarious.

I think think this is one of the greatest comics ever! I read them all day. So you should read them too!
Edward a sixth grader

After floundering trying to understand abstract computer science issues such as computability, NP-complete, Turing machines, with very basic math skills, I came across this book. I thought it would just introduce concepts of fuzzy logic, neural nets, and genetic programming. Pleasantly surprised that, in doing the above, the fundamental concepts are quite lucidly explained. A real mathematician would be disappointed with the lack of full proofs and mathematical rigor, but for the non- or novice mathhead, this is a wonderful find.

After reading this book, I would echo the mostly positive reviews of this book offered by others below. As noted by others, *The Importance of Being Fuzzy* is an accessible intro to fuzzy logic, issues surrounding the limitations of computability (Godel/Turing/NP-completeness), neural networks, and genetic algorithms.

Arturo Sangalli tries to give just enough of a taste of the technical details of the topics mentioned above to balance the need to be accessible without dumbing things down too much. Sangalli writes about the theoretical, historical, and applicability issues surrounding so-called *soft computing* (fuzzy logic, etc.).

One of the things I found interesting about Sangalli's writing style is that he writes very efficiently. By that I mean that he manages to discuss all of the very complicated concepts mentioned above in a succinct and efficient way without losing clarity and accessibility. He included 4 brief appendixes dealing with various concepts mentioned in the main text in a more formal way (for those who are interested).

In short this book is by far the most accessible account of fuzzy logic, NP-completeness, neural networks, and genetic algorithms. Fortunately, this reader-friendliness does NOT come at the price of having a dumbed down account. [As for Godel/Turing computability issues, there are a variety of other contenders for accessible accounts (e.g., *Godel, Escher, Bach*).] No wonder this book won the 1998 Association of American Publishers Award for Best Professional/Scholarly Book in Computer Science.

Finally, I take issue with the hostile review from Ontario, Canada. The obvious purpose of this book is to offer an intelligent yet readable introduction to *soft computing* issues. It is completely unfair to bash this book because it does not engage in a sufficient degree of name-dropping. In fact, one piece of name-dropping by the hostile reviewer -- his complaint that the book did not mention Gregory Chaitin -- is really off-base since there really is no need in a book like this to deal with AIT/Kolmogrov complexity [the limits of computability issues can be dealt with sufficiently by citing Godel/Turing/Church and NP-completeness]. I strongly believe that the merits of a book should be based on rational criteria and not on tangential issues.

Though it is slim, TIBF gives a nice overview of some cutting-edge (as of 1998) developments in computer science, having to do with fuzzy logic, neural networks, and genetic algorithms. The treatment is generally superficial, but just deep enough to give some impression of the mathematics that undergirds these developments. The writing is informal and mostly entertaining. Overall, TIBF reads like an expanded piece of popular science journalism, punctuated by an occasional impenetrable detail. It is well-worth a read, and useful, in addition, for the many references it provides to key literature in the field.

The Importance of Being Fuzzy is a book not just about fuzzy logic but also genetic algorithms and the limits of computers. I found the introductory chapters on fuzzy logic to be accessible but found later chapters very hard to follow. I think this is because the author attempts to go to a depth not really appropriate for the general audience this book is meant for. For example the chapter on the limits of computers could be the subject of a whole book and would need to be to be adequately explained. Still this book is worth reading for it's depictions of the many successful uses that fuzzy logic has been put to.

This book is a very basic overview of many topics on the borderline between classical mathematics and computer science. Since the book's title prominently uses the word "fuzzy" one would expect more than just a general overview of the field yet that is really all that is presented here. After several chapters intermixing history and some (very basic) theory, the author moves on to other topics such as the halting problem.

A general overview of the "new math" is not necessarily a bad thing but there are numerous glaring omissions from the book. I fail to see how anyone who is providing a basic review of fuzzy theory and then, later in the same book, neural networks could fail to include mention of Perlovsky. Or, better yet, how anyone talking about the evolution of mathematics to include problems and solutions that involve computing could leave out Wolfram who has numerous papers and was the developer of Mathematica software used by many.

But the worst omission occurs with the discussion of the halting problem. I fail to see how you can discuss Godel, Church and Turing without including Chaitin unless you either don't like him personally or are a really really poor researcher. Considering this book is likely destined for some high school shelves then this omission is even more unforgiveable given the fact that Chaitin's work is quite accessible.

Then there is the fact that there is no mention of Kolmogorev or algorithmic information theory. Again, even a simple overview should have appeared here since it appears the book's intent is a teaser about the new avenues of work being explored in mathematics.

Oh well, most of the information presented is relatively clear although I must say that Klir and Yuan do a better job with fuzzy theory in their book. All in all there is not much to reccommend this one.

After spending some time trying to grasp the concepts of fuzzy logic and fuzzy sets, I found this book. This is THE book to start if you want to get a quick introduction to what fuzzy logic is, and how to use fuzzy sets as a tool. I highly recommend this book if you are having problems following other books in fuzzy logic. There is an example for every concept that is introduced, making it really easy to follow and understand

This 136 page book provides a brief introduction to fuzzy logic and applications. However, I have to disagree with the comment that symbols are always defined when used, as many are not.

Also, I think the book may have suffered in translation, as there are quite a few errors, especially in the translation of formulas. For example, on page 27 is an incontrovertable mangling of De Morgan's laws. In other places, symbols are left out, subscripts and superscripts are inexplicably moved around, and shading for graphs and tables is mentioned many places in the text but mysteriously not present in the graphs and tables referred to.

Fortunately, Tanaka goes over the same topic from multiple prespectives, in most cases allowing the reader to figure out what is going on. As an introduction, this book would definitly have benefited from a table of symbols. However, overall, a good introduction to (or review of) the topic.

I purchased this book to gain enough information to read a technical paper. Fuzzy logic is new to my industry (petroleum) and my 1970's education did not provide any background. The book took less than an evening to absorb and provided more than enough understanding of the notation and basic operations that I was able to read my paper and start building an interest in deploying Fuzzy logic in my daily work. Other books are needed to fully apply the methodology. However, sufficient demonstration of basic fuzzy arithmetic was provided to know that 2 times 3 divided by 2 is not necessarily 3.

I shared the book with a mathematically oriented associate and she had similar experiances.

Overall, a great introduction with just enough information for a cursory review and enough detail to help determine need or interest for a more detailed presentation.

This book gives you an excellent introduction to Fuzzy Logic Concepts, Reasoning and Applications.

I am a Practitioner of Industrial Process Control, and was looking for a book to learn about Fuzzy Logic. The book did it in a simple way, with many examples and explanation for every topic to make even easier my introduction to this area.

I was impressed by the fact that most symobology used in the book is defined during its first use. There are a few symbols like 'sup' on page 38 that I'm still unclear about.

There are five basic chapters in the book:
1 Introduction
2 Fuzzy Set Theory
3 Fuzzy Relations
4 Fuzzy Reasoning
5 Fuzzy Logic Control

Chapter 1 is a brief two page intro to the concept. The chapter on Fuzzy Set Theory gets into the basics. I've read the descriptions of Fuzzy Logic in MathLab's Fuzzy Logic module and so was prepared for most what is in this chapter. As such, I'm still somewhat unclear as how Cartesion Products and Extension Principles are applicable to the whole concept of Fuzzy Logic.

In the chapter on Fuzzy Relations, further use of extensions is used along with the properties of composition. Simple matrix math is used in some cases to arrive at results in some of the examples.

The fourth chapter, which is about Fuzzy Reasoning, includes reasoning based upon Mamdani's Direct Method, Takagi & Sugeno's Fuzzy Modelling, and the Simplified Method. It is in this chapter where the earlier mechanisms of composition are utilizied. Defuzzification, which is final step of any fuzzy logic process, is lightly described with a brief reference to the standard centroid calculation.

The final chapter is light on formulas, and offers up a high level description of the superiority of fuzzy logic over PID controllers, and how the former can help the latter obtain better control in some situations.

After having taken a first read of this book, I'll have to go through it again to see if I can better relate Fuzzy Relations to the remainder of the book. In addition, now that I've got a better grasp on fuzzy symbology, I believe I'm ready to move on to the more heavy duty books of the subject area.