Discussion
The centroid method of defuzzification can be represented by the following algebraic expression :
Answer: B
The centroid method is \(z^{*} = \dfrac{\int \mu(z).z\,dz}{\int \mu(z)\,dz}\), option (B), where \(\mu\) stands for \(\mu_{\underset{\sim}{c}}\), the membership function of the aggregated output.
The centroid (centre of gravity or centre of area) method takes the crisp output to be the point that balances the area under the membership curve: the integral of \(\mu(z)\) times z, divided by the total area, the integral of \(\mu(z)\).
Option (A), the point where membership reaches its maximum, is the max-membership (height) principle. Option (C), a weighted sum over the centres \(\bar{z}\) of the individual output sets, is the weighted average method. Option (D), the midpoint (a + b)/2 of an interval, is the mean of maximum when the maximum is a plateau from a to b.
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