Generally, solving a multicriteria problem consists in finding the “most appropriate” solution taking into account a set of criteria. It is possible to summarize this process in 4 steps. First, potential actions (alternatives) must be enumerated then we must draw up a list of criteria to be considered. Alternatives are evaluated relative to the criteria in order to generate the performances matrix. Finally, we must proceed to a multicriteria aggregation (Ben Mena, 2000).
Multicriteria Aggregation
The multicriteria aggregation is the operation of finding a formal representation of the actions performances in relation to criteria. The origin of the performances aggregation problem is that there is rarely a consensus between the criteria in comparing alternatives and conflicts are frequently noted. Therefore, it is important to find a compromise in the light of these conflicts by looking for a decision rule for constructing a preference relation between actions.
For any pair of alternatives 
, a decision rule defines a binary predicate 
which value is a function of the performances vectors 
and 
(Grabisch & Perny, 2002). When 
takes its values in the set 
, we talk about a “net” preference relationship and there is talk of a “fuzzy” preference relationship when the predicate values belong to the interval 
. Indeed, the evaluation of the preference 
is done in two operations, namely, the aggregation
of performances 
and 
and the comparison (
) of alternatives 
and 
through their performances vectors. The association of these two functions logically leads to two different orders in which 
is an increasing function of its arguments and 
an increasing function of its first argument and decreasing of the second and 
for any real 
:
(1)In the “Aggregate then Compare” (AC) approach, the aggregation function 
allows grouping actions performances in values representing their global performances for a unique synthetic criterion. The comparison function 
allows measuring and evaluating the preference degree between global performances (Grabisch & Perny, 2002). The weighted sum is a good example of the “AC” approach.
The “Compare then Aggregate” (CA) approach compares actions performances in pairs. Thus, for each pair of actions and each criterion, a partial preference index is defined. The aggregation function allows aggregating partial preference indexes even if they are associated to different criteria. The ELECTRE family is a classic example of the “CA” approach.