You get into the shower. The water is too hot. You increase the cold water. The water is now too cold. You turn up the hot water. After two or three iterations the water is just right. An alternative might be to spend a fair amount of money on a valve that will only allow water to flow when a specific water temperature is reached. The Fuzzy Logic (or former) approach is less efficient, however far less expensive. An excellent discussion, Fuzzy Logic For "Just Plain Folks" presents a non-PhD explanation
Fuzzy Logic functions on the concept that unique values cannot be used efficiently for control situations. In the example above – you cannot preset the knobs. Fuzzy logic allows you to modify the environment until the correct goal is reached. One business approach that can use fuzzy logic is evaluating a process or company. You know that the value is greater than zero. You also know that the value cannot exceed $100,000. The answer lies in a continuum between the two values. You can assign a probability to both extreme values and extrapolate the correct value.
A Google Search on the term Fuzzy Logic returns almost 3,000,000 hits. The first page of the search that is returned yields some fascinating information.