Positive Approximation and Rule Extracting in Incomplete Information Systems

Set approximation is a kernel concept in rough set theory. In this paper, by introducing a notion of granulation order, positive approximation of a target set under a granulation order is defined in an incomplete information system and its some useful properties are investigated. Unlike classical rough set theory, this approximation deals with how to describe the structure of a rough set in incomplete information systems. For a subset of the universe, its approximation accuracy is monotonously increasing with a granulation order becoming longer. This means that a proper family of granulations can be chosen for a target concept approximation according to user requirements. Furthermore, an algorithm based on the positive approximation, called MABPA II, is designed for decision-rule extracting and a practical example is employed to illustrate its mechanism.