Towards a formal theory of aggregation

The problem of aggregation is addressed from the standpoint of symmetry preservation, thus defining a formal approach to aggregation. Two methods for aggregating from the heterogeneous Quadratic Lanchester formalism to the homogeneous Quadratic Lanchester formalism are presented. Intensive aggregation, which is independent of the Force Strength components, is appropriate for situations where the Attrition Rate Coefficient tensor is dense and irreducible. Extensive aggregation, an approximate methodology which is dependent on the Force Strength components, may be used when these conditions are not satisfied. An example of aggregation to either the heterogeneous or the homogeneous formalism from platform level simulation results is presented and supplemented with an explicit script of a symbolic algebra program exercise. Finally, the Formal Aggregation methodology is compared with the AMTI Potential method.