The Seven Truths Of Fuzzy Logic

Seven Truths

The Seven Truths of Fuzzy Logic: There is nothing fuzzy about Fuzzy Logic. Fuzzy Logic is different from Probability. Designing the Fuzzy Sets is very easy. Fuzzy systems are stable, easily tuned, and can be conventionally validated. Fuzzy systems are different from and complementary to neural networks. Fuzzy Logic "ain't just process control anymore". Fuzzy Logic is a representation and reasoning process.

An excerpt from Computer Design that recently appeared in Reprinted with permission.

By Earl Cox (, April 1992.

The idea that fuzzy logic is fuzzy or intrinsically imprecise is one of the most commonly expressed fables in the fuzzy logic mythos. This wide-spread belief comes in two flavors, the first holds that fuzzy logic violates common sense and the well proven laws of logic, and the second, perhaps inspired by its name, holds that fuzzy systems produce answers that are somehow ad-hoc, fuzzy, or vague. The feeling persists that fuzzy logic systems somehow, through their handling of imprecise and approximate concepts, produce results that are approximations of the answer we would get if we had access to a model that worked on hard facts and crisp information. Nothing could be further from fact.

There is nothing fuzzy about fuzzy logic, Fuzzy Sets differ from classical or crisp sets in that they allow partial or gradual degrees of membership. We can see the difference easily by looking at the difference between a conventional (or "crisp") set and a fuzzy set. Thus someone 34 years, eleven months, and twenty eight days old is not middle aged. In the Fuzzy representation, however, we see that as a person grows older he or she acquires a partial membership in the set of Middle Aged people, with total membership at forty years old.

But there is nothing ambiguous about the fuzzy set itself. If we know a value from the domain, say an age of 35 years old, then we can find its exact and unambiguous membership In the set, say 82%. This precision at the set level allows us to write fuzzy rules at a rather high level of abstraction. Thus we can say, if age is middle-aged, then weight is usually quite heavy; and means that, to the degree that the individual's age is considered middle aged, their weight should be considered somewhat heavy. A weight estimating function, following this (very simple) rule might infer a weight from age through the following fuzzy implication process.

Much of the discomfort with fuzzy logic stems from the implicit assumption that a single ``right'' logical system exists and to the degree that another system deviates from this right and correct logic it is in error. This ``correct'' logic, of course, is Aristotelian or Boolean logic. But as a logic of continuous and partial memberships, Fuzzy Logic has a deep and impressive pedigree. Using the metaphor of the river, Heraclitus aptly points out that a continuous reasoning system more correctly maps nature's logical ambiguities. From his dictum that all is flux, nothing is stationary, he developed a rudimentary multi-valued logic two hundred years before Aristotle. Recently, Bart Kosko, one of the most profound thinkers in fuzzy logic, has shown that Boolean logic is, in fact, a special case of fuzzy logic.