Second Order Measures for Uncertainty Processing

Abstract

Uncertainty processing methods are analysed from the viewpoint of their sensitivity to small variations of certainty factors. The analysis makes use of the algebraic theory which defines the function for combining partial certainty factors by means of a group operation of the ordered Abelian group over the interval of uncertainty. Two approaches are introduced: (a) sensitivity analysis of the inference network and (b) calculation of second order probabilities. Sensitivity functions are defined as partial derivatives of the combining function with respect to their arguments. Based on the sensitivity functions, we define the path sensitivity which measures the sensitivity of a larger part of the inference network. If a set of samples of certainty factors is available instead of a single value, the second order probability distribution can be approximated by the distribution of an average value. It is shown that the parametric form of the distribution is completely determined by the combining function.