Prioritized aggregation operators and their applications

Multicriteria decision problems having a prioritization relationship between the criteria arises in situations in which a decrease in satisfaction to a higher priority criteria can't be readily compensated by an increase in satisfaction to a lower priority criteria. A typical example of this is the relationship between safety and cost. We consider criteria aggregation procedures for use in this kind of situation. We suggest that the prioritization between criteria can be modeled by making the weights associated with a criterion dependent upon the satisfaction of the higher priority criteria. We implement this using a prioritized scoring operator. We show how the lack of satisfaction to a higher order criteria blocks the possibility of compensation by lower priority criteria. We show that in the special case where the prioritization relationship among the criteria satisfies a linear ordering we can use a prioritized averaging operator.