On the interpretation of certainty factors in expert systems

Despite the strong theoretical foundation the Bayesian probabilistic approach to model uncertainty in medicine meets many difficulties at the implementation step. One of these difficulties is related to a large amount of conditional probabilities to be assessed and in many cases this task was recognised to be practically insoluble. The MYCIN certainty factors model is a widely distributed pragmatical approach for modeling reasoning under uncertainty that substantially simplifies the problem, at the sacrifice of theoretical soundness. One can determine certainty factors as a function of prior and posterior probability. However, this approach is only consistent with the modularity axiom for certainty factors for tree-structure inference networks, which is rarely true for practical applications. In this paper we abandon the requirement of a direct probabilistic interpretation of certainty factors and build a model of propagation of uncertainty in terms of absolute belief and belief updates. We describe our model for propagating uncertainty in terms of matrix multiplication with specifically defined addition and multiplication which correspond to parallel and sequential combinations of certainty factors. It is possible to define these operations in such a manner that they form a field, and therefore to obtain some useful properties. Finally we present a method of determining certainty factors from statistical data using nonlinear regression and illustrate it with a leukemia diagnostics problem.