The straightforward efforts of Japan to commercialize fuzzy logic are striking compared to the disconnected U.S. efforts. Before discussing the Japanese use of fuzzy logic, a brief explanation of what fuzzy logic is and is not is in order. Professor Lotfi Zadeh of the University of California, Berkeley, is credited with "inventing" fuzzy logic, usually traced to his 1965 paper. Fuzzy logic is to be distinguished from crisp logic, where given items are either members of a given set or they are not (objects or events fall into some category or they do not). In fuzzy logic, an item (object or event) can have any degree of membership m (possibility, degree of relative truth) from 0 to 1 in a fuzzy set, that is, a fuzzy variable, category, or term like TALL: for example, a person may be 0.3, meaning "not very," or 0.7, meaning "quite," TALL.

It is fundamental to distinguish fuzzy membership from probability, where before the fact the chance of an occurrence can fall anywhere between 0 and 1, but after the fact, the occurrence either happened or it did not. By contrast, in fuzzy logic membership remains between 0 and 1 (a table is always a chair with, say m = 0.4, if it can be sat upon). The transformation from a continuous or discontinuous variable to a fuzzy (categorical) variable is the membership function, which resembles a probability density function, but is not.

In applying fuzzy logic, one maps the particular values in physical variables of some real object or event, say the height and speed of a person, to memberships on corresponding fuzzy variables. In addition, one must have a set of rules (e.g., if TALL and FAST, then GOOD AT BASKETBALL), where the conjunction "and" calls for the minimum membership of the person being considered in the separate sets for TALL and for FAST (the conjunction "or" calls for the maximum). Thus, for any given person, application of every rule about GOOD AT BASKETBALL (there may be other rules about experience, etc.) yields an output membership value, and in the end, these outputs can be averaged to determine whether to sign that person up for the team. The attractiveness of fuzzy logic is that it allows the use of heuristics couched in the natural language or fuzzy terms of real people. Few basketball scouts know about differential equations!

Fuzzification (transformation from the crisp logic domain to the fuzzy one and back again to yield a real-world decision) is in order to make use of the fuzzy rules that characterize real world knowledge. Recent work (some by this author) has shown how crisp and fuzzy knowledge can be combined to provide better answers than by using only one or the other. For example, if deterministic algebraic rules or probabilistic properties are known, then linear programming or Bayesian inference can and should be used to the extent that they can.

Zadeh's term "fuzzy" was unfortunate for the West and fortunate for the East. In the West it had an inhibiting effect; government agencies and technical firms alike found Zadeh's ideas humorous and ridiculed him. One research funder told the writer that no project of his would ever be intentionally "fuzzy." In Japan and China, in stark contrast, the ideas caught on immediately and were taken quite seriously; "fuzzy" is comfortable there and fit the culture. After a little research, it was also shown that fuzzy logic adapts well to control of nonlinear systems and systems with unmodeled parameters, which have long proved unstable when attempts were made to control them by continuous linear controllers.

Both Matsushita and Omron, for example, were quick to adapt fuzzy controllers to cameras, washing machines, and other consumer devices, and they proudly advertise the fact. Japan is already marketing a variety of fuzzy computer chips capable of handling transformations for large sets of fuzzy rules (many simple parallel computations) at blazing speed.

While Western researchers have finally appreciated the potential of fuzzy logic (IEEE now has a transactions on fuzzy systems), the semantic reaction is still taking its toll on adoption of fuzzy ideas in Western industry. This is truly an instance where deep cultural factors have determined the speed of adoption of a new technology.

Published: March 1996; WTEC Hyper-Librarian