Decision attitude

Representative weighting vector W of dimension N of the OWA operator

Monarchical & Optimistic

$w_N=1$

Monarchical & Pessimistic

$w_1=1$

Monarchical & Neutral

for $N=2k+1$ $w_{quotient\left(N/2\right)+1}=1$

Democratic & Neutral

$w_i=1/N$ $i=1,\cdots ,N$

Semi Monarchical & Neutral

$w_1=w_N=0.5$

Semi Democratic & Neutral

$w_i=1/\left(N-2\right)$ and $i=2,\cdots ,N-1$

Semi Monarchical/Democratic & Neutral

$w_1=w_N=0.25$

$w_i=0.5/\left(N-2\right)$ and $i=2,\cdots ,N-1$

Monarchical & Towards Optimistic

For $N=2k+1$ $w_i=1$ and quotient $\left(N/2+1\right)<i<N$ (the greater the i the more the optimism)

For $N=2k$ $w_i=1$ and $N/2<i<N$ (the greater the i the more the optimism)

Monarchical & Towards Pessimistic

For $N=2k+1$ $w_i=1$ and $1<i<quotient\left(N/2+1\right)$ (the greater the i the more the optimism)

For $N=2k$ $w_i=1$ and $1<i<N/2$ (the smaller the i the more the pessimism)

Semi Monarchical & Towards Optimistic

$w_1=1-\alpha$ $w_N=\alpha$ and $0.5<\alpha <1$ the greater the $\alpha$ the more the optimism.

An alternative choice can be $w_N=w_{N-1}=0.5$

Semi Monarchical & Towards Pessimistic

$w_1=\alpha$ $w_N=1-\alpha$ and $0.5<\alpha <1$ the greater the $\alpha$ the more the pessimism.

An alternative choice can be $w_1=w_2=0.5$

Democratic & Towards Optimistic

$w_i=2i/\left(N\left(N+1\right)\right)$

Democratic & Towards Pessimistic

$w_i=2\left(N+1-i\right)/\left(N\left(N+1\right)\right)$

Semi Democratic & Towards Optimistic

For $N=2k$ $w_i=2/N$ $i>N/2$

For $N=2k+1$ $w_i=2/\left(N+1\right)$ $i>N/2$

Semi Democratic & Towards Pessimistic

For $N=2k$ $w_i=2/N$ $i\le N/2$

For $N=2k+1$ $w_i=2/\left(N+1\right)$ $i\le N/2+1$