The entropy effect and sensitivity analysis in rule-based expert systems

In a typical business environment, information is seldom known or believed with certitude and most data tend to be either unknown or in the form of forecasts or estimates. Yet decisions are still required to be made in a timely and efficient manner. When this decision making is supported by expert or knowledge-based systems, a critical requirement is the ability of these systems to reason with missing and uncertain information. This paper addresses the question of when it is worthwhile to capture and to add one or more unknown facts to the knowledge base of a production rule expert system. The paper argues that an unknown fact should be entered into the knowledge base if such an action alters the certainty associated with the final recommendation of the expert system. An entropy effect in large knowledge-bases is hypothesized and, using a network representation of the knowledge base, empirically verified through a simulation. The entropy effect suggests that the effects of additional information on final outcomes may be negligible after the propagation of uncertainties through the knowledge-base. Because of the presence of the entropy effect, it becomes necessary to estimate a priori the value of acquiring additional information. A computationally simple procedure for determining the sensitivity of the certainty of any node with respect to a change in certainty at another node is described; this procedure can be utilized to assess the value of additional information prior to its acquisition.