Partial Order
This is a preference structure for Modeling Preferences in MCDA that includes $J$ - the Incomparability relation.
Assume:
- there are different experts $\{1, 2, 3\}$
- they evaluate 4 projects $a, b, c, d$
- investment $a$ is preferred to investment $b$ if estimates from $a$ are higher than from $b$ (or $a$ dominates $b$)
- i.e. there is Unanimity between the experts
|
$a$ |
$b$ |
$c$ |
$d$
|
1
|
10 |
8 |
7 |
6
|
2
|
9 |
7 |
5 |
6
|
3
|
12 |
8 |
9 |
4
|
We can infer the following relations:
- $a \ P \ b$ because all three experts agree
- but $b \ J \ c$:
- 1st expert say $b \ P \ c$
- but 3rd say $c \ P \ b$
- therefore we cannot compare $a$ and $b$
so we have partial order:
- $P$ is transitive
- and $J$ is not empty
Sources