Evaluation Using Fuzzy Logic Sample Clauses

Evaluation Using Fuzzy Logic. Every top-down atomic tree or other “Boolean” decision tree can be rewritten as a set of classification rules using Boolean logic. For instance, the tree in Figure 4.5 can be written as: If (T > 25) л (WF < 16) then class := Swimming (4.13) and If (T 25) V (T > 25 л WF /< 16) then class := Sailing, (4.14) where T stands for Temperature and WF stands for Wind Force. If we would do the same for the similar fuzzy decision tree in Figure 4.6 we would get: and If (T = Warm) л (WF = Light) then class := Swimming (4.15) If (T Warm) V (T = Warm л WF Light) then class := Sailing. (4.16) Temperature = Warm no yes Sailing WindForce = Light no yes Sailing Swimming Figure 4.6: Example of Figure 4.5, recast as a fuzzy decision tree. However, since the result of a fuzzy atom is a fuzzy membership value rather than a Boolean value we use fuzzy logic operators. By replacing the Boolean operators with their fuzzy logic counterparts defined in Equa- tions 4.7, 4.8 and 4.9, Equations 4.15 and 4.16 become: and μSwimming := μ(T=Warm) × μ(WF=Light) (4.17) μSailing := μ(T=Warm) + (μ(T=Warm) × μ (WF/=Light)). (4.18) − Note that we can use μAVB = μA + μB instead of Equation 4.9 because the sum of the membership values for the possible target classes is always 1 for our decision (sub)trees. We also no longer have a simple “If then” statement but a fuzzy membership function defining each class.
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