| The sloping down line of membership function mG passes
through points (10, 1) and (30, 0). Let us say that the equation of the line
is:
mG(x)=ax+b We apply this equation for x=10, mG =1 and x=30, mG =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 mG is: mG(x)=-0.05x+1.5 for 10< x<30 If x=19, like in the example, we substitute and find mG(19)=0.55 We work similarly to derive the equation for the sloping up part of membership function mA. We note that it passes through points x=30, mA=1 and x=10, mA=0. This equation turns out to be: mA(x)=0.05x-0.5 for 10< x<30 Upon substitution with x=19 we obtain: mA(19)=0.45
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