Comparing Fusors within a Category of Fusors

Category Theory is used to describe a category of fusors. The category is formed from a model of a process begining with an event and leading to the final labeling of the event. Although many techniques of fusing information have been developed the inherent relationships among different types of fusion techniques (fusors) have not yet been fully explored. In this paper, a foundation of fusion is presented, definitions developed, and a method of measuring the performance of fusors is given. Functionals on receiver operating characteristic (ROC) curves are developed to form a partial ordering of a set of classifier families. The functional also induces a category of fusion rules. The treatment includes a proof of how to find the Bayes optimal classifier (or Bayes Optimal fusor, if available) from a ROC curve.