Rough Set Approach with Imperfect Data Based on Dempster-Shafer Theory

Original rough set theory deals with precise and complete data, even though real applications frequently contain imperfect information. Missing values are typical imperfect data studied in rough set research. Many ideas have been proposed in the literature to solve the issue of imperfect data, but hardly a single solution is sufficient for multiple types of imperfect data containing imprecision and uncertainty. The paper models some basic relations between objects with respect to an imperfect attribute value using the Dempster-Shafer theory of evidence, and defines uncertain relations between objects with multiple imperfect attribute values by combining basic relations defined in a single attribute. It also proposes new rough set models based on these basic relations and discusses the properties of these models.