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Consider a Takagi-Sugeno – Kang (TSK) Model consisting of rules of the form:

If $x_1$ is $A_{i1}$ and $\dots$ and $x_r$ is $A_{ir}$

THEN $y=f_i(x_1, x_2, \dots , x_t)=b_{i0} + b_{i1} x_1 + \dots + b_{ir}x_r$

assume, $\alpha _i$ is the matching degree of rule $i$, then the total output of the model is given by:

  1. $y=\sum \limits_{i=1}^L \alpha_i f_i (x_1, x_2, \dots , x_r)$
  2. $y=\dfrac{\sum \limits_{i=1}^L \alpha_i f_i (x_1, x_2, \dots , x_r)}{\sum \limits_{i=1}^L \alpha _i}$
  3. $y=\dfrac{\sum \limits_{i=1}^L f_i (x_1, x_2, \dots , x_r)}{\sum \limits_{i=1}^L \alpha _i}$
  4. $y=\underset{i}{\text{max}} [\alpha _i f_i (x_1, x_2, \dots , x_r)]$
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