Few of us would disagree that the world is difficult to understand clearly. In the mid-sixties Lofti Zadeh concluded that 'hardly anything is precise if we examine it with sufficient care'. Zadeh studied the mathematical techniques of the time and found that none of them allowed a satisfactory framework with which to deal with the imprecision's of reality. Fuzzy logic originated from the requirement for sound mathematical techniques to describe imprecision and uncertainty.
Fuzzy logic is constructed around the basic idea of the fuzzy set.
Conventional set theory is based upon boolean sets - i.e. a value either belongs to a certain set or it doesn't. This works well for numerical theory - a number is either negative or positive, a certain value is either real or complex. For instance, consider the definition that cars going at 70mph or more belong to the set 'fast'. At first glance this looks like a reasonable proposition but looking in more detail shows a lack of flexibility in this definition. This is the primary problem with boolean sets, their absolute nature does not reflect the way the world actually is.