Consistent Family of Criteria
A family of criteria in an MCDA problem should satisfy the following three properties:
- Exhaustivity
- Cohesion
- Non-Redundancy
These properties together form a consistent family of criteria
Notation
- $A = {a, b, c, …}$ - set of alternatives
- $G = {g_1, …, g_k}$ - set of criteria
- $a_1 \ P \ a_2$ - preference relation between two alternatives
- $a_1 \ I \ a_2$ - indifference relation between two alternatives
Properties
Exhaustivity
$\forall g_i$ s.t. $g_i (a) = g_i (b) \Rightarrow a \ I \ b$
Cohesion
$\forall a, b \in A$ if
- $\exists g_i \in G: g_i(a) > g_i(b)$ and
- $\forall g_j \in A, g_j \ne g_i: g_j(a) = g_j(b)$
- then $a \ P \ b$
Alternative formulation:
- The Dominance principle should be respected
Non-Redundancy
$G$ is not redundant if removal of any $g_i \in G$ leads to violation of exhaustivity or cohesion
Links
- http://www.lamsade.dauphine.fr/~bouyssou/TranspaOrbel16.pdf