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Consider a standard additive model consisting of rules of the form of

If $x$ is $A_i$ AND $y$ is $B_i$ THEN $z$ is $C_i$. Given crisp inputs $x=x_0, \: y=y_0$ the output of the model is

  1. $z=\Sigma_i \mu_{A_i} (x_0) \mu_{B_i} (y_0) \mu_{C_i} (z)$
  2. $z=\Sigma_i \mu_{A_i}(x_0) \mu_{B_i} (y_0)$
  3. $z=\text{centroid } (\Sigma_i \mu_{A_i} (x_0) \mu_{B_i} (y_0) \mu_{C_i} (z))$
  4. $z=\text{centroid } (\Sigma_i \mu_{A_i} (x_0) \mu_{B_i} (y_0)$
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Best answer

option c

STANDARD ADDITIVE MODEL (SAM)  includes the centroid defuzzification technique. here 

IF x is AND y is THEN z is
Given crisp inputs x= x0, y = y0, 

z=centroid(ΣiμAi(x0)μBi(y0)μCi(z))

source : http://shodhganga.inflibnet.ac.in/bitstream/10603/134769/9/09_chapter%203.pdf


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