Fuzzy logic is the system that can not be modeled with linear differential equations. Rules and memberships sets are used to make a decision. This rules concern how fast to fill a bucket, based upon how full it is. A simple verbal rule se as following:

• If (bucket is full) then (stop filling)

• If (bucket is half full) then (fill slowly)

• If (bucket is empty) then (fill quickly)

From the figure above there is question “what does it mean when the bucket is empty, half full or full?” We can define sets that indicate when something is true (1), false (0) or a bit of both (1-0). Refer to picture below:

Consider the bucket is full set. When the height is 0, the set membership is 0. Nobody will think the bucket is full. As the height increase more people think the bucket is full until they all think the bucket is full. Notice that the angle function relates the valve angle to the fill rate. The sets are shifted to the right.

An example of a fuzzy logic controller is for controlling a servomotor as shown on picture below. This controller rules examine the system errors and the rate of error change to select a motor voltage. In this example the set memberships are defined with straight line.