Fuzzy Logic for Beginners [Paperback]

 

 

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In terms of the aims of the book (as an introductory text) it was informative, and does lay the foundation for further investigation and learning. The book is filled with a mixture of diagrams and illustrative cartoons to aid the reader in their understanding, and this does give some personality to a rather dry subject.

However the language is clearly translated from what I imagine is the original Japanese text, and has some 'interesting' elements. If you can get over this, and I personally enjoyed it by the end of the book, then I would recommend it.

The good will is there. What is missing is a good translationa and a competent editor/publisher! The book gives you the basics of fuzzy logic. This would be an excellent book, were it not for the many mistakes it contains, which make it difficult to follow.

I agree with my predecessors that to some extent (0.5) this book is all right. It was aimed as an introductory text and in fact it does so. But there are some issues you should keep in mind reading it especially if you have no first-order logic background.

1) Wrong examples. The author often gives an example of `beautiful woman' as a way to explain the idea of fuzziness and compares it to classical logic claiming that it cannot deal with it. I disagree with that and let me explain why. Suppose your buddy shows you a picture of a woman and asks if she is beautiful. In fuzzy logic you have a choice between 0 and 1 (0 means she's not beautiful, 1 means she definitely is beautiful, in between means she is to some degree beautiful) but in binary logic you have only true and false. Is it the case that you may not know if she is or isn't beautiful? I don't think so. But the situation may totally change if your friend told you that he finds her beautiful and that she is his fiancée. What I mean is that fuzzy logic can be a good to provide an explanation to social behaviour. But the author does not mention it. For him the fuzzy logic is superior in every case.

Furthermore, the author claims that the fuzzy set theory is superior to set theory in explaining the phenomenon of being, for example, a beautiful woman or middle-aged. Is it so? Why set theory fails? I can't see that. The only difference is that fuzzy set theory deals with subjectively assigned numbers. But set theory can explain it as well as fuzzy. Let's have a look. What does it mean `to be middle-aged'? Probably for many of us that means different time scale. For X it means to be 35-55 years old, for Y it is to be 30-40 years old. So why can't we express it in set theory? In this example you have two sets X and Y having numbers {35,...,55} and {30,...,40} respectively. The intersection is the solution that explains what does it mean to be middle-aged person for X and Y (ie.35-40). I reckon fuzzy set theory would give similar answer. He totally misses the point.

2) Next claim is that apart from probability theory only fuzzy logic deals with uncertainty. Is it so? What about game theory? GT is about 20-30 years older and has better foundations than fuzzy logic. What about many valued logic (ie. Three-valued logic proposed by Lukasiewicz about 40 years before fuzzy logic)? It deals with uncertainty (half-true statements) as good as fuzzy logic does.

3) It also seems that the author has little idea about first-order logic or as expressed in fuzzy logic notation he has 0.3 idea of it. He makes wrong assumptions that lead to wrong conclusions, specifically in regards to implication. Let's have a look at his example: 'if a woman is beautiful then she has a short life' (pp.47-48). The he considers the fact that X is pretty. This suppose to mean that if X is pretty then X has short life and he claims that 'binary-based symbolic logic can derive no conclusion from incomplete premises.' Really? We are able to construct a set P with pretty objects and B with beautiful objects and the intersection of them gives us a subset with objects that are pretty and beautiful and it holds true that we can derive a conclusion that if X is pretty (and X is beutiful) then X has short life. Also for those not trained in first-order logic: A->B is true when A is true and B is true, or when A is false and B is true or when both A and B are false. Not only when A and B are true as the author says on page 45.

4) Bad translation and misspelled names. For all of you who wondered who are Ripunitz or Alstoteres let me explain. The first is Leibnitz the second is Aristotle. The book desperately needs an editor.

However, the topic of fuzziness is no doubt fascinating only this book can't cope with it. Fuzzy Thinking: The New Science of Fuzzy Logic by Bart Kosko or Fuzzy Logic: The Revolutionary Computer Technology That is Changing Our World by Daniel McNeill are most likely better choice for beginners than this book.

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