Page 48 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

36 Chapter 1

Figure 1-18. Yinput as the crisp input for the variable Y

Similarly the Yinput belongs to the set Ymedium with fuzzy membership 0.7
and belongs to the set Ylarge with 0.2 as shown in the figure given below

Step 2: Fuzzy input to fuzzy output mapping using fuzzy base rule

Fuzzy base rule is the set of rules relating the fuzzy input and fuzzy output
of the fuzzy based system. Let us consider the Fuzzy Base Rule as shown in
the table given below.

Table 1-1. Fuzzy Base Rule

Ysmall Ymedium Ylarge
small Zmedum Zmedium Zsmall
Xmedium Zmedium Zlarge Zlarge
Xlarge Zlarge Zlarge Zmedium

Thus Fuzzy input set Xsmall = {Xinput (0.7) }
Xmedium = {Xinput (0.3) }
Xlarge = {Xlarge( 0 )

Ysmall = {Yinput (0) }
Ymedium = {Yinput (0.7) }
Ylarge = {Xlarge(0.2)
Fuzzy output set is obtained in two stages.

1. Intersection of Fuzzy sets
• Xsmall ∩ Ysmall = Zmedium ={Zoutput(0)}
• Xsmall ∩ Ymedium = Zmedium ={Zoutput(0.7)}
• Xsmall ∩ Ylarge = Zsmall ={Zoutput(0.2)}
• Xmedium ∩ Ysmall = Zmedium ={Zoutput(0)}

• Xmedium ∩ Ymedium = Zlarge={Zoutput(0.3)}