Ancient Greece

The success of modern mathematics is largely due to the efforts of Aristotle and the philosophers who preceded him. In their efforts to devise a concise theory of logic, and later mathematics, the so-called "Laws of Thought" were invented. One of these, the "Law of the Excluded Middle," stated that every proposition must either be True or False, A or not-A, either this or not this. For example, a typical rose is either red or not red. It cannot be red and not red. Every statement or sentence is true or false or has the truth value 1 or 0. Even then, there already were strong and immediate objections to this proposal.

In fact, almost two centuries earlier, Buddha saw the world filled with contradictions, that things could be a certain degree true and a certain degree false at the same time. However, it was Plato who laid the foundation for what would become fuzzy logic, indicating that there was a third region (beyond True and False) where these opposites "tumbled about.

The world's getting fuzzier

In the early 1900s, Lukasiewicz came and proposed a systematic alternative to the bi-valued logic(bivalence) of Aristotle. He described a three-valued logic, which can best be translated as the term `possible', and assigned it a numeric value between True and False. Knuth, a former student of Lukasiewicz proposed a three-valued logic apparently missed by Lukasiewicz, whiched used an integral range [-1, 0 +1] rather than [0, 1, 2]. Nonetheless, this alternative failed to gain acceptance, and has passed into relative obscurity.

It's heeere
It was not until relatively recently that the theory of fuzzy logic was discovered. Lotfi A. Zadeh, a professor of UC Berkeley in California, soon to be known as the founder of fuzzy logic observed that conventional computer logic was incapable of manipulating data representing subjective or vague human ideas such as "an atractive person" or "pretty hot". Fuzzy logic, hence was designed to allow computers to determine the distinctions among data with shades of gray, similar to the process of human reasoning. In 1965, Zadeh published his seminal work "Fuzzy Sets" which described the mathematics of fuzzy set theory, and by extension fuzzy logic. This theory proposed making the membership function (or the values False and True) operate over the range of real numbers [0.0, 1.0]. Fuzzy logic was now introduced to the world.
Although, the technology was introduced in the United States, the scientist and researchers there, ignored it mainly because of its unconventional name. They refused to take something which sounded so child-like seriously. Some mathematicians argued that fuzzy logic was merely probability in disguise. Only stubborn scientists or ones who worked in discrete continued researching it.

While the US and certain parts of Europe ignored it, fuzzy logic was excepted with open arms in Japan, China and most Oriental countries. It may be suprising to some that the world's largest number of fuzzy researchers are in China with over 10,000 scientists. Japan, though currently positioned at the leading edge of fuzzy studies falls second in manpower, followed by Europe and the USA. Hence, it can

be said that the popularity of fuzzy logic in the Orient reflects the fact that Oriental thinking more easily accepts the concept of "fuzziness". And because of this, the US, by some estimates, trail Japan by at least ten years in this forefront of modern technology.

Return to Main Menu