Fuzzy Logic/the Discovery of a Revolutionary Computer Technology and How It Is Changing Our World [Hardcover]

Classical logic forces all actions to be described by a rigid sequence of two option rules. By applying enough such rules, it is possible to eventually reach a reasonable approximation to the problem in question. However, such a method is cumbersome at best, so in 1964, Lotfi Zadeh, a professor of electrical engineering, invented a new reasoning system base on imprecise rules. Since the values are now placed within specified ranges, the system was given the unfortunate name "fuzzy ." Eventually ignored and at times vilified by the academic community in the United States, fuzzy logic is now beginning to be widely used in commercial products.
In another instance of what seems to be the most common business theme of the decade of the '80s, it was Japanese industry that took the American ideas and made them commercially viable. Many products now incorporate fuzzy reasoning systems, with no end in sight regarding the spectrum of applications. The performance gains of fuzzy logic over other options is at times astounding.
Equally surprising is the simplicity of fuzzy reasoning. Most events in the human experience are not sharply demarcated. Night does not "fall," but slowly floats down like an aging helium balloon. Fuzzy systems mimic this by assigning a numeric value to qualifying words such as "very ," "slightly ," and "remotely ." The most common scale uses the range from zero to one inclusive. Since zero can be considered FALSE and one TRUE, classical logic is a limiting subset of fuzzy logic. For example, the phrase "very possible" could be assigned a truth value of 0.90, "slightly possible" a value of 0.05, and "remotely possible" a value of 0.005. Fuzzy OR then takes the largest value of the two variable, AND the minimum of the two and the negation is computed by taking one minus the fuzzy value.
This book introduces the basic notions of fuzziness, but concentrates more on the history as an ignored discipline and the recent commercial successes. It is amazing to learn that the vast majority of "fuzzy thinkers" are found in Asia. Comparisons between the differences in Western and Eastern philosophy are made in an attempt to explain this. For example, the Japanese language is inherently much more vague than western languages.
If you are interested in learning the first notions of fuzzy reasoning, this book is a good non-technical place to start. And if the applications continue to grow, that interest may become a required taste.

Published in Journal of Recreational Mathematics, reprinted with permission.

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