3. (18 pts) Consider a fuzzy inference system with input domain U = (-1,1] *N and output domain W = (-1, 1)*N. a) Draw the input domain decomposition of U by five fuzzy sets A1,..., As with peak points - 1*N, --3*N, ON, .3*N, and 1*N. Put your drawing on the graph paper on the next page. b) Draw the output domain decomposition of W by five fuzzy sets C1,..., Cs with peak points - 1*N, -.5*N, ON, .5*N, and 1*N. Put your drawing on the graph paper on the next page. Consider the rule base if X is A, then 2 is Cs if X is A, then 2 is C if X is Ag then Z is Cs if X is A4 then 2 is C if X is As then 2 is Cs c) What is the membership of input .5 *N in each of the fuzzy sets A1,..., As? N=24 d) Using weighted averaging defuzzification, what is the response for input .5*N? e) What is the membership of input .3 *N in each of the fuzzy sets A1,..., As? f) Using weighted averaging defuzzification, what is the response for input .3*N? 8) Draw the piecewise linear function determined on U x W by this rule base. Clearly mark each point where the line segments change. Put your drawing on the graph paper on the next page