On Probability of Matching in Probability Based Rough Set Definitions

The original rough set theory deals with precise and complete data, while real applications frequently contain imperfect information. A typical imperfect data studied in rough set research is the missing values. Though there are many ideas proposed to solve the issue in the literature, the paper adopts a probabilistic approach, because it can incorporate other types of imperfect data including imprecise and uncertain values in a single approach. The paper first discusses probabilities of attribute values assuming different type of attributes in real applications, and proposes a generalized method of probability of matching. It also discusses the case of continuous data as well as discrete one. The proposed probability of matching could be used for defining valued tolerance/similarity relations in rough set approaches.