Slides for Fuzzy Sets, Ch. 2 of Neuro-Fuzzy and Soft Computing
Slides for Fuzzy Sets, Ch. 2 of Neuro-Fuzzy and Soft Computing
Slides for Fuzzy Sets, Ch. 2 of Neuro-Fuzzy and Soft Computing
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>Neuro</strong>-<strong>Fuzzy</strong> <strong>and</strong> S<strong>of</strong>t <strong>Computing</strong>: <strong>Fuzzy</strong> <strong>Sets</strong><br />
Least-Square Estimators<br />
Where: A is an m*n matrix which is:<br />
θ is n*1 unknown parameter vector:<br />
A<br />
=<br />
θ =<br />
⎡f<br />
⎢<br />
M<br />
⎢<br />
⎣⎢<br />
f<br />
1<br />
1<br />
⎡θ<br />
⎢<br />
⎢<br />
⎢⎣<br />
θ<br />
1<br />
M<br />
(u<br />
(u<br />
n<br />
⎤<br />
⎥<br />
⎥<br />
⎥⎦<br />
1<br />
m<br />
) Lf<br />
n<br />
) Lf<br />
n<br />
(u<br />
1<br />
(u<br />
) ⎤<br />
⎥<br />
⎥<br />
) ⎥⎦<br />
m<br />
<strong>and</strong> y is an m*1 output vector:<br />
y<br />
⎡y<br />
=<br />
⎢<br />
M<br />
⎢<br />
⎢⎣<br />
y<br />
1<br />
m<br />
⎤<br />
⎥<br />
⎥<br />
⎥⎦<br />
<strong>and</strong> a<br />
T<br />
i<br />
=<br />
[ f (u ),...,f (u )]<br />
1<br />
i<br />
n<br />
i<br />
13<br />
A θ = y ⇔ θ= A -1 y (solution)
Change language