A description of competing fusion systems

A mathematical description of fusion is presented using category theory. A category of fusion rules is developed. The category definition is derived for a model of a classification system beginning with an event set and leading to the final labeling of the event. Functionals on receiver operating characteristic (ROC) curves are developed to form a partial ordering of families of classification systems. The arguments of these functionals point to specific ROCs and, under various choices of input data, correspond to the Bayes optimal threshold (BOT) and the Neyman–Pearson threshold of the families of classification systems. The functionals are extended for use over ROC curves and ROC manifolds where the number of classes of interest in the fusion system exceeds two and the parameters used are multi-dimensional. Choosing a particular functional, therefore, provides the qualitative requirements to define a fusor and choose the best competing classification system.