Determining certainty factors with the analytic hierarchy process

Certainty factors are intended to measure the certainty of expert system rules. Since certainty factors represent a change in the probability of a hypothesis, given additional information about an event, a rule's certainty factor depends on the difference between posterior and prior probabilities. Developers of the MYCIN expert system (originators of the certainty factor concept) abandoned Bayes' Theorem and the p-function because they felt there were large areas of expert knowledge and intuition that, although amenable in theory to the frequency analysis of statistical probability, defied rigorous analysis, in part, because experts resisted expressing their reasoning process in coherent probabilistic terms. The Analytic Hierarchy Process (AHP) facilitates the practical acquisition of experts' knowledge and intuition in a way that produces ratio scale likelihoods with a theoretical basis that conforms to Bayes Theorem and the p-function. Although AHP is well known by decision analysts, it has not yet been widely applied to expert systems applications. We show how AHP can be used to develop prior and posterior probabilities and how these probabilities can be used to calculate certainty factors for expert system rules.