Decision making with probabilities, weighted averages and OWA operators

Abstract

We develop a new method for decision making based on the use of probabilities, weighted averages and ordered weighted averaging (OWA) operators. We analyze a method that it is able to deal with several aggregation structures thus obtaining a more general formulation that represents the information in a more complete way. We introduce a new aggregation operator that aggregates a wide range of other aggregation operators. Therefore, we can include in the same formulation a wide range of concepts and representing how relevant they are in the aggregation. We call it the unified aggregation operator. By using this aggregation operator we can deal with a wide range of complex structures, for example, we can aggregate in a decision making problem several structures of probabilities, weighted averages and OWA operators. Thus, the information we provide is more complete because in real world problems the information comes from different sources and this needs to be considered in the aggregation process. We study the applicability of this new approach and we see that it is very broad because real world problems are better assessed with this new model. We focus on a multi-person decision making example where we use several structures of probabilities, weighted averages and OWA operators, thus representing the subjective and the objective information and the attitudinal character in a more complete way.