In most synthesis evaluation systems and decision-making systems, data are represented by objectsand attributes of objectswith a degree of belief. Formally, these data can be abstracted by the formobjects; attributes; P,where P represents a kind degree of belief between objects and attributes,such that, P is a basic probability assignment. In the paper, we provide a kind of probabilityinformation system to describe these data and then employ rough sets theory to extract probabilitydecision rules. By extension of Dempster-Shafer evidence theory, we can get probabilities ofantecedents and conclusion of probability decision rules. Furthermore, we analyze the consistencyof probability decision rules. Based on consistency of probability decision rules, we provide aninferencemethod to finish inference of probability decision rules, which can be used to decide theclass of a new object x. The conclusion points out that the inferencemethod of the paper not onlydeals with precise information, but also imprecise or uncertain information as well.
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