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We describe multicriteria aggregation and discuss its central role in many modern applications. The concept of aggregation imperative is introduced to indicate the description of how the individual criteria satisfactions should be combined to obtain the overall score. We focus on a particular type of aggregation imperative called prioritized aggregation that is characteristic of situations where lack of satisfaction to criteria denoted as higher priority cannot be compensated by increased satisfaction by those denoted as lower priority. We discuss two approaches to the formulation of this type of aggregation process. One of these uses the prioritized aggregation operator, and the second is based on an integral-type aggregation using a monotonic set measure to convey the prioritized imperative.