(4) Our goal is to design a motor speed controller for an air conditioner. Define input and output variables: Let X be the temperature in Fahrenheit and let Y be the motor speed of the air conditioner. Define linguistic terms of the linguistic variables temperature (X) and motor speed (Y) and associate them with fuzzy sets: 5 linguistic terms / fuzzy sets on X (Cold, Cool, Just Right, Warm, and Hot) and 5 linguistic terms / fuzzy sets on Y (Stop, Slow, Medium, Fast, and Blast). The membership functions of these variables are shown in the following figure:
Input fuzzy sets
Output fuzzy sets
Assign a motor speed set to each temperature set
\begin{itemize}
\item If temperature is cold then motor speed is stop
\item If temperature is cool then motor speed is slow
\item If temperature is just right then motor speed is medium
\item If temperature is warm then motor speed is fast
\item If temperature is hot then motor speed is blast
\end{itemize}
Assuming Mamdani inference system, determine the motor speed output fuzzy sets and determine the corresponding crisp value using weighted average method in each of the following cases:
1- temperature = 65° F
2- temperature = 63° F