Behavioral Analysis of Aggregation in Multicriteria Decision Aid

Let us consider a finite set of alternatives A = {a, b, c, . . .} and a finite set of criteria N = {1, . . . , n} in a multicriteria decision making problem. Each alternative a ∈ A is associated with a profile xa = (x1, . . . , x a n) ∈ IR, where, for any i ∈ N , xi represents the partial score of a related to criterion i. We assume that all the partial scores are defined according to the same interval scale, that is, they are defined up to the same positive linear transformation. Particularly, this will enable us to embed the scale in the unit interval [0, 1]. From the profile of any alternative a ∈ A, one can compute a global score M(xa) by means of an aggregation operator M : IR → IR which takes into account the weights of importance of the criteria. Once the global scores are computed, they can be used to rank the alternatives or select an alternative that best satisfies the given criteria. Until recently, the most often used aggregation operators were the weighted arithmetic means, that is, operators of the form