Page 49 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

1. Artificial Intelligence 37

• Xmedium ∩ Ylarge = Zlarge ={Zoutput(0.2)}
• Xlarge ∩ Ysmall = Zlarge ={Zoutput(0)}
• Xlarge ∩ Ymedium = Zmedium ={Zoutput(0)}
• Xlarge ∩ Ylarge = Zsmall ={Zoutput(0)}

2. Union of Fuzzy sets

• Zsmall = U(Zoutput(0.2), Zoutput(0))={ Zoutput(0.2) }
• Zmedium = U(Zoutput(0), Zoutput(0.7), Zoutput(0),Zoutput(0))
= {Zoutput (0.7)}
• Zlarge = U(Zoutput(0.3), Zoutput(0.2), Zoutput(0))={Zoutput(0.3)}

Thus Fuzzy output based on the framed fuzzy base rule is given as

Zsmall = {Zoutput(0.2)
Zmedium = {Zoutput(0.7}
Zlarge = {Zoutput(0.3)}

Step 3: Fuzzy to Crisp conversion for the output variable Z using
Centroid method

Figure 1-19. Defuzzification