m_G(x)=ax+b

  We apply this equation for x=10, m_G =1 and x=30, m_G =0:

1 =a10+b    (1)

0 =a30+b    (2)

(1)-(2):  1=-20a =>a=-0.05   (3)

(3) into (2): b= -30(-0.05)=>b=1.5

So the equation for the sloping down part of membership function m_G is:

m_G(x)=-0.05x+1.5  for    10< x<30

If x=19, like in the example, we substitute and find  m_G(19)=0.55

We work similarly to derive the equation for the sloping up part of membership function m_A. We note that it passes through points x=30, m_A=1 and x=10, m_A=0. This equation turns out to be:

m_A(x)=0.05x-0.5  for    10< x<30

Upon substitution with x=19 we obtain:

m_A(19)=0.45