. In a public transport system there is often a need for speed control. In the Delhi Metro System, for example, the train speed cannot go too far beyond a certain target speed or the trains will have trouble stopping at a desired location in the station. Let Fuzzy set A = “speed way over target” on a universe of target speeds T = {60, 70, 85, 90} is defined as: A = {(t: triangle (t; 65, 80, 95)), t ε T}. Another, Fuzzy set B = “apply brakes with high force” on a universe of braking pressure S = {10, 20, 30, 40} is defined as: B = {(s: triangle (s; 0, 40, 60)), s ε S}.
a. Find fuzzy sets A and B.
b. For the proposition R1 = if speed is way over target then apply brakes with high force, find the fuzzy relation.
c. For the proposition R2 = if speed is very way over target then apply brakes with extremely high force, find the fuzzy relation.
d. At what force would the brakes be applied if speed is at 90 units using both rules R1 and R2 from part b. and c. respectively?
e. Defuzzify the output obtained in previous part using Centroid method.