Table 5 The ordered aggregated preference and asymmetry matrices
\({\mathbf {V}}\) | \(I_2\) | \(I_1\) | \(I_3\) | \(I_4\) |
|---|---|---|---|---|
(a) Preference matrix | ||||
\(I_2\) | 0.0 | 2.0 | 2.0 | 3,0 |
\(I_1\) | 1.0 | 0.0 | 2.0 | 3,0 |
\(I_3\) | 1.0 | 1.0 | 0.0 | 3,0 |
\(I_4\) | 0.0 | 0.0 | 0.0 | 0,0 |
\(\sum\) | 2.0 | 3.0 | 4.0 | 9.0 |
N\(^\text {o}\) | 1 | 2 | 3 | 4 |
Opposite preferences (E)=1+1+1=3 | ||||
\({\mathbf {A}}\) | \(I_2\) | \(I_1\) | \(I_3\) | \(I_4\) |
|---|---|---|---|---|
(b) Asymmetry matrix | ||||
\(I_2\) | 0,0 | 1/3 | 1/3 | 1,0 |
\(I_1\) | \(-\)1/3 | 0,0 | 1/3 | 1,0 |
\(I_3\) | \(-\)1/3 | \(-\)1/3 | 0,0 | 1.0 |
\(I_4\) | \(-\)1.0 | \(-\)1.0 | \(-\)1.0 | 0.0 |
\(\sum\) | \(-\)5/3 | \(-\)1.0 | 1/3 | 3.0 |
N\(^\text {o}\) | 1 | 2 | 3 | 4 |
Sum of the lower triangular=\(-\)4 | ||||