ON THE INTERPRETATION OF CERTAINTY FACTORS IN EXPERT-SYSTEMS

Despite the strong theoretical foundation the Bayesian probabilistic a pproach to model uncertainty in medicine meets many difficulties at th e 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 certai nty factors model is a widely distributed pragmatical approach for mod eling reasoning under uncertainty that substantially simplifies the pr oblem, at the sacrifice of theoretical soundness. One can determine ce rtainty factors as a function of prior and posterior probability. Howe ver, this approach is only consistent with the modularity axiom for ce rtainty factors for tree-structure inference networks, which is rarely true for practical applications. In this paper we abandon the require ment of a direct probabilistic interpretation of certainty factors and build a model of propagation of uncertainty in terms of absolute beli ef and belief updates. We describe our model for propagating uncertain ty in terms of matrix multiplication with specifically defined additio n and multiplication which correspond to parallel and sequential combi nations of certainty factors. It is possible to define these operation s in such a manner that they form a field, and therefore to obtain som e useful properties. Finally we present a method of determining certai nty factors from statistical data using nonlinear regression and illus trate it with a leukemia diagnostics problem.