When fuzzy logic was first introduced, it was done to some amount of hype and fanfare as the Next Big Thing that would revolutionize computing. It never really did this, because that was never the intent. Instead, it is now most widespread amongst control systems, where you want some amount of self-conciousness when it comes to how close you are to the target. Fuzzies are popular in systems such as air conditioners, rice cookers, and light meters.

To create a fuzzy controller for an air conditioner, you set up a number of nodes on your axis, and give them values, i.e. -20 degrees below the set temperature is really cold, -10 degrees is cold, -5 [degrees is cool, 0 degrees is just right, 10 degrees is warm, and 20 degrees is way too hot. You then program the machine to work at different intensities for each of these temperature values. The fuzzy part comes in when the temperature is say, 8 degrees below the set temperature. The machine will determine that it is 40% cool and 60% cold, and respond accordingly.

There has been some interesting research in combining fuzzy logic with that other hyped technology, neural networks. Basically, you can make a neural net train itself to arrange the nodes and intensities of the fuzzy system so that it will give optimal control.

Like proportional control systems, the fuzzy logic controller I have described above can get really hosed if you have some delay in your system's feedback. It can be set to compensate for this by adjusting non-proportionally when the system is close to the target, but there are times when it can still be beaten by the good old PID control.