Alternative Representations of OWA Operators

It is known that OWA operators appear to be particular cases of Choquet integral with respect to a suitable fuzzy measure. Recently, it has been shown that fuzzy measures can be expressed in three different, completely equivalent forms (called representations), among which the so-called interaction representation. It has been shown that only the interaction representation makes sense for a decision maker in multicriteria or multiattribute or multiperson problems, with close links to the Shapley value in cooperative game theory. In this paper we will give the three representations of an OWA operator, with emphasis on the interaction representation, in order to give new insights into its meaning in aggregation. We will also give best linear and 2nd order approximations of OWA operators.