Information fusion with uncertainty modeled on topological event spaces

We investigate probability and belief functions constructed on topological event spaces (without requiring complementation operation as in the definition of Borel sets). Anchored on the Lattice Theory, and making use of the correspondence of distributive lattice and topology, we propose a hierarchical scheme for modeling fusion of evidence based on constructing the lattice of topologies over a given sample space, where each topology encodes context for sensor measurement as specified by the basic probability assignment function. Our approach provides a rigorous mathematical grounding for modeling uncertainty and information fusion based on upper and lower probabilities (such as the Dempster-Shafer model).