Customer Reviews

Fuzzy Set Theory: Foundations and Applications

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I'm quite impressed with the clarity and style of Klir's introduction to fuzzy set theory. The book starts with the absolute basics of classical logic and then builds to classical set theory. This half of the book is actually far superior to any of my other logic books since it puts all the truely relevant material together in a very cogent manner.

The second half of the book goes into the details of fuzzy logic and set theory while maintaining the easy style and excellent examples of the previous sections. This book, while intended as a textbook, is quite readable for those who just wish to have better knowledge of fuzzy logic. I suspect that many of the Aristotelian-based classical logicians will be hard-pressed to surpass Klir's clear explanations for their home turf.

Klir delves into the philosophical basis for the existence of fuzzy logic and I feel he does an excellent job. Haack should really read this again and then reconsider her grand statement that "I believe truth does not come in degrees" with some of the open-mindedness evidenced by Klir.

Highly recommended.

Wow. It's a real shame that this book costs so much. The explanations of classical set theory and fuzzy set theory are simple, clear, and not too hard to understand. I would have liked to have seen some answers to selected problems in this text. Still, for anyone who wants to learn fuzzy set theory or review the basics, here is a very excellent place to go.

The book discusses alpha cuts, strong alpha cuts, classical set theory, fuzzy set theory, classical relations, fuzzy relations, classical logic, multivalued logics and their fuzzy systematization, and more. It also contains a short reference list for further study.

I use this book for a course in the first semester. The students are not familiar with deeper mathematical ideas (not even with the one of a limit), but still thanks to Klir's book they are able to follow a kind of up-to-date mathematics. One of the advantages of the book is that all the principal ideas (operations, relations, logic) are firstly explained in the crisp case and then in the fuzzy case.