C++ Neural Networks and Fuzzy Logic: Preface

1.  (0.75) ¥ (0.4) = 0.4

2.  (0.25) ¥ (0.4) = 0.25

3.  (0.75) ¥ (0.6) = 0.6

4.  (0.25) ¥ (0.6) = 0.25

By using the fuzzy rule base and the strengths assigned previously, we find the rules recommend the

following output values (with strengths) for HeatKnob:

1.  AGoodAmount (0.4)

2.  VeryLittle (0.25)

3.  ALot (0.6)

C++ Neural Networks and Fuzzy Logic:Preface

Step Five: Defuzzify the Outputs

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4.  ALittle (0.25)

Now we must combine the recommendations to arrive at a single crisp value. First, we will use the fuzzy Or

method of defuzzification. Here we use a disjunction or maximum operator to combine the values. We obtain

the following:

     (0.4) ¦ (0.25) ¦ (0.6) ¦ (0.25) = 0.6

The crisp output value for HeatKnob would then be this membership value multiplied by the range of the

output variable, or (0.6) (10−0) = 6.0.

Another way of combining the outputs is with the centroid method. With the centroid method, there are two

variations, the overlap composition method and the additive composition method. To review, we have the

following output values and strengths.