Consistency of Probability Decision Rules and Its Inference in Probability Decision Table

In most synthesis evaluation systems and decision‐making systems, data are represented by objects and attributes of objects with a degree of belief. Formally, these data can be abstracted by the form ( objects; 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 probability information system to describe these data and then employ rough sets theory to extract probability decision rules. By extension of Dempster‐Shafer evidence theory, we can get probabilities of antecedents and conclusion of probability decision rules. Furthermore, we analyze the consistency of probability decision rules. Based on consistency of probability decision rules, we provide an inference method to finish inference of probability decision rules, which can be used to decide the class of a new object x ′ . The conclusion points out that the inference method of the paper not only deals with precise information, but also imprecise or uncertain information as well.