This solution is not always works ideally. Somewhy Piecewise functions can have gaps while plotting. Check out this code, It can even be some faster
MembershipFunction[center_, mid_] :=
Module[{S, pi},
pi[x_, a_, c_] := Piecewise[{
{S[x, c - b, c - b/2, c] /. {b -> (a + c)/2}, x <= c},
{1 - S[x, c, c + b/2, c + b] /. {b -> (a + c)/2}, x > c}}];
S[x_, a_, b_, c_] := Piecewise[{
{0, x < a},
{2 ((x - a)/(c - a))^2, a <= x <= b},
{1 - 2 ((x - c)/(c - a))^2, b < x <= c},
{1, x > c}}];
a = 4 (3/4 center - mid);
ListLinePlot[Table[{x, pi[x, a, center]}, {x, 0, center*2, center/50}]]
]
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