Problem 2. Sketch the membership function pm (I) =e_'l'(x_)\" for [1 =2 , n =2 , and :1 =3 for the support set S =[0,6]+ On this sketch separately show the shaded areas that represent the following fuzziness measures given by M Jr, M 2 and M 3: _ f(x)=#A(X) for #A(x)0.5 (a) M1f(x)dx where =l,uA(x) for #A(x)>0.5 (b) M: =J|pA(x)pt,2(x)|dx S where \"A\": isthe acutof ,uAUc) for a=1f2 to) M3 =I|m(x)#2(x)| dx S where I is the complement of the rzzy set A. Evaluate the values of M1,M2 and M3 for the given membership function. i. Establish relationships between M1,M2 and M3. ii. Indicate how these measures can be used to represent the degree of fuzziness of a membership function. iii. Compare your results with the case 1:], a = 3 , and n = 2 for the same support set, by showing the corresponding fuzziness measures on a sketch of the new membership function