A graph-based evidence theory for assessing risk

The increasing exploitation of the internet leads to new uncertainties, due to interdependencies and links between cyber and physical layers. As an example, the integration between telecommunication and physical processes, that happens when the power grid is managed and controlled, yields to epistemic uncertainty. Managing this uncertainty is possible using specific frameworks, usually coming from fuzzy theory such as Evidence Theory. This approach is attractive due to its flexibility in managing uncertainty by means of simple rule-based systems with data coming from heterogeneous sources. In this paper, Evidence Theory is applied in order to evaluate risk. Therefore, the authors propose a frame of discernment with a specific property among the elements based on a graph representation. This relationship leads to a smaller power set (called Reduced Power Set) that can be used as the classical power set, when the most common combination rules, such as Dempster or Smets, are applied. The paper demonstrates how the use of the Reduced Power Set yields to more efficient algorithms for combining evidences and to application of Evidence Theory for assessing risk.