Aggregation operators defined by k-order additive maxitive fuzzy measures

It is well known that the Choquet and Sugeno integrals w.r.t. a discrete fu zzy measure can be considered as aggregation operators. In this paper, we s tudy in detail two special cases of symmetric fuzzy measures, i.e. fuzzy me asures of which the values only depend upon the cardinality of the argument s. The first case is that of a symmetric k-order additive fuzzy measure, i. e. a fuzzy measure of which the Mobius transform vanishes in sets with card inality greater than k. A new increasing sequence of binomial OWA operators is introduced. It is recalled that weighted sums of aggregation operators, with possibly negative weights, may also lead to aggregation operators. Th e Choquet integral w.r.t. a symmetric k-order additive fuzzy measure is the n characterized as such a weighted sum of the first k binomial OWA operator s. The second case is that of a symmetric k-order maxitive fuzzy measure, i .e. a fuzzy measure of which the possibilistic Mobius transform vanishes in sets with cardinality greater than k. The Sugeno integral w.r.t. a symmetr ic k-order maxitive fuzzy measure is then characterized as a weighted maxim um of the last k order statistics.