The speed limit is 60mph on an open highway with no traffic. Here are three obvious rules to control your car with a fuzzy control system.

(a) If you are going too fast, then slow down.

(b) If you are going close to the speed limit, stay at roughly the same speed.

(c) If you are going too slow, then speed up. We interpret "slow down" and "speed up" as negative acceleration (deceleration) and positive acceleration.

 Let's measure acceleration in (miles per hour) per second. 

(a) Draw and label fuzzy membership functions for the antecedents and consequents of these fuzzy control rules. Label your graphs clearly with the corresponding fuzzy linguistic variables, velocities, and acceleration

(b) Evaluate the instantaneous response (i.e. acceleration) of your system when i. you are going the speed limit, and ii. you’re going 50 mph.

(c) Repeat the problem using clipped membership functions in the defuzzification step.