Earlier in this chapter the recursive least squares algorithm was demonstrated using training set $Z$ of Table 7.1.
(a) Modify the input membership functions centers to the following values and develop a fuzzy model for the Z of Table 7.1 using the RLS algorithm (perform two cycles). Note that the remaining rule-base parameters are the same as those used in the text, e.g.,
$$
\begin{aligned}
& \sigma_j^i=2 \quad \text { and } \quad \hat{\theta}(0)=\left[\begin{array}{l}
0.3647 \\
8.1775
\end{array}\right] \\
& c_1^1=1 \quad c_1^2=3 \\
& c_2^1=3 \quad c_2^2=6
\end{aligned}
$$
(b) In part (a) the input membership function centers were slightly different than those used in the text but the spreads were the same values as those used in the text. Now change the spreads to the following values, $\sigma_1^1=3, \sigma_1^2=2, \sigma_2^1=1, \sigma_2^2=2$, and the remaining values should be the same as in part (a). Develop a fuzzy model for the $Z$ of Table 7.1 using the RLS algorithm (perform two cycles.)