C++ Neural Networks and Fuzzy Logic: Preface

1.  AGoodAmount (0.4)

2.  VeryLittle (0.25)

3.  ALot (0.6)

4.  ALittle (0.25)

We use the strength value and fill in the particular triangular membership function to that strength level. For

example, for the first rule, we fill the triangular membership function, AGoodAmount to the 0.4 level. We

then cut off the top of the triangle (above 0.4). Next we do the same for the other rules. Finally we align the

truncated figures as shown in Figure 16.6 and combine them according to the overlap composition method or

the additive composition method (Kosko). You can see the difference in these two composition methods in

Figure 16.6. The overlap method simply superimposes all of the truncated triangles onto the same area. You

can lose information with this method. The additive method adds the geometrical figures on top of each other.

Figure 16.6

  Defuzzification with the Centroid approach: Overlap and Additive composition.

In order to get a crisp value, you take the centroid or center of gravity, of the resulting geometrical figure. Let

us do this for the overlap method figure. The centroid is a straight edge that can be placed through the figure

to have it perfectly balanced; there is equal area of the figure on either side of the straight edge, as shown in

Figure 16.7. Splitting up the geometry into pieces and summing all area contributions on either side of the

centroid, we get a value of 5.2 for this example. This is already in terms of the crisp output value range:

     HeatKnob = 5.2

Figure 16.7

  Finding the centroid.

C++ Neural Networks and Fuzzy Logic:Preface

Step Five: Defuzzify the Outputs

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This completes the design for the simple example we chose. We conclude with a list of the advantages and

disadvantages of FLCs.