Formalizing classes of information fusion systems

This paper provides an outline of a formalization of classes of information fusion systems in terms of category theory and formal languages. The formalization captures both the inputs/outputs of a fusion system and the fusion processing algorithms. The paper also introduces a notion of subclass, which is used to compare classes of fusion systems, whether they are different or one is a special case of another. Two examples of classes of fusion systems formalized in the paper are data fusion and decision fusion; decision fusion is shown to be a subclass of data fusion. A number of other classes of fusion systems are defined. The formalization is extended by adding the notion of measure of effectiveness, which is then used to prove that one of the classes (so called overlapping system) is at least as efficient as a single-source system. And finally it is shown how data association can be formalized in this framework. While at first the formalization could be used by information fusion scientists to formally define various types of fusion systems and then to prove theorems about properties of such systems, it is expected that it should lead to the development of tools that could be used by software engineers to formally derive designs of fusion systems.