The Importance of Being Fuzzy

Rating:
Summary: Wonderful
Review: 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.

Rating:
Summary: Great intro to fuzzy logic, computability, neural nets, & GA
Review: 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.

Rating:
Summary: Defuzzification In Action!
Review: Great introduction for the general interest reader. Sangalli clarifies Fuzzy Set Logic with ease.

Rating:
Summary: Complexity made simple
Review: If you want to find out how a computer works, you won't get much help by taking a look under the cover. What you see is a floor of chips, a maze of wires and a little fan to keep things cool - not a pretty sight, but then neither is the box itself. When Steve Jobs decided to colour his iMACs and use transparent perspex so that we can see the innards, he was responding to this drab ugliness with a touch of rouge and a dab of eye shadow. Ultimately however, if you want to find the soul of the computer, what makes it fast or slow, clever or stupid, efficient or a nuisance, you will have to get inside its mathematics.

Most people know that the mathematics behind computers has something to do with binary arithmetic and things called bits and bytes and logic gates. What they may not know is that there is a well-established science of computability; it even has its own Einstein in the person of the tragic English genius Alan Turing.

In this book, Canadian academic Arturo Sangalli describes Turing's work, and examines three mathematical techniques which modern research is using in attempts to make computers more efficient and possibly more intelligent. All three approaches started life as esoteric mathematical ideas and lay dormant for some time before computer researchers began to use them.

The most interesting and most easily understood is what is known as fuzzy logic. This may seem like a contradiction in terms, but as Sangalli points out, it is a logic of fuzziness, not a logic which is itself fuzzy. In its broadest sense, it is synonymous with the mathematical theory of fuzzy sets.

The concept of a Set was one of the core elements of the New Maths of the 1970s which many parents will gratefully recall as the excuse they were able to give for not being able to help their children with school mathematics. I won't try to change that situation at this late stage, beyond saying that a set has to be precisely determined - you cannot have vaguely defined sets like "tall people" or "funny television programs" or "interesting books."

The mathematical theory of fuzzy sets was taken down from the shelf and dusted off some years ago by computer engineers, particularly in Japan where the government persuaded a consortium of local heavies - Matsushita, Canon, Hitachi, and Mitsubishi among others - to invest $50 million in the Laboratory for International Fuzzy Engineering Research (LIFE). The result has been that most electronic goods now produced in Japan contain what an advertisement currently running on television calls "fuzzy thingys."

To give an idea of how fuzziness is used in computer programs, consider the way a child balances a stick upright on the palm of one hand. The feat requires a complex combination of movements and adjustments and feedback. How can a computer be taught to do the trick?

What computer engineeres have done is to construct a mechanical model controlled by a computer which has been programmed with the kinds of rules which a child might give to explain how he/she was performing the trick. So, there is rule which says "If the stick is balanced, do not move your hand," and another "If the stick is slightly tilted away from you and falling slowly, move your hand forward, but not too quickly."

Phrases like "slightly tilted" or "falling slowly" or "not too quickly" would be anathema to conventional mathematics, but fuzzy mathematics is able to put a range of possible numbers on them, and the computer can be taught to understand and respond.

Surprisingly, to balance the rod, only five other rules along with the two above are needed. The system works perfectly every time and appears to be extraordinarily robust, working equally well with rods of different lengths and weights. Moreover, if one rule is omitted or minor changes are made to a rule, the system still works most of the time - a far cry from the annoyance which is the constant companion of computer programmers who see their program crash as a result of a missing comma or semi-colon somewhere in the middle of metres of code.

Of course, the solution is as much a triumph of smart electronics as of clever computer programming. But the point is that it demonstrates a program which works well even though it has been given imprecise instructions. Just as with the child, the logic may be fuzzy, but the result is not.

By 1993, there were more than 600 consumer products in Japan which used fuzzy chips. And the Japanese hit a marketing jackpot when they found that their country was happy to accept the English word fuzzy rather than its local equivalent. Everything from washing machines to wheelchairs to photocopiers and cameras had fuzzy logic chips - not to mention the television set which the chap in the advertisement so enthusiastically demonstrates to his friend by opening and closing his curtains while their kids wonder at the childlike joy of their elders.

"Computers can do only what we tell them to do," is a paraphrase of the famous statement by Ada Lovelace, daughter of Lord Byron and one of the pioneers of computer programming. With fuzzy logic, Lady Lovelace's dictum may not be as close to Holy Writ as we thought.

Well done, Dr Sangalli.

Rating:
Summary: Great intro to fuzzy logic, computability, neural nets, & GA
Review: 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.

Rating:
Summary: Basic and missing some important items...
Review: 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.