OWA aggregation with an uncertainty over the arguments

We discuss the OWA aggregation operation and the role the OWA weights play in determining the type of aggregation being performed. We introduce the idea of a weight generating function and describe its use in obtaining the OWA weights. We emphasize the importance of the weight generating function in prescribing the type of aggregation to be performed. We consider the problem of performing a prescribed OWA aggregation in the case when we have a probability distribution over the argument values. We show how we use the weight generating function to enable this type of aggregation. Next we consider the situation when we have a more general measure based uncertainty over the argument values. Here again we show how we can use the weight generating function to aid in performing the prescribed OWA aggregation in the face of this more general type of uncertainty. Finally we look at the task of obtaining a weight generating function from a given set of OWA weights.