Research on Uncertainty Measurement for Covering Rough-Vague Set

In this paper, by the research of covering rough set theory, rough-vague set model based on covering is presented by integrating rough set theory and vague set theory. Covering rough-vague set is a generalized model of rough set. In order to measure the model´s uncertainty perfectly, firstly, we must consider the uncertainty produced by granular size of covering. So knowledge capacity measurement M(C) is defined to measure the uncertainty of classification capability of covering. This measurement can reflect the essential character of knowledge classification. The thinner the covering knowledge granularity is, the bigger the knowledge capacity of the covering. At the same time, compared with information entropy (the traditional method), the calculation of M(C) is simple. Then we use roughness to measure the size of borderline area of rough-vague set. Considering all the causes of uncertainty of covering rough-vague set, we introduce the definition of K-roughness to measure the model´s uncertainty effectively by combining knowledge capacity measurement and roughness. Last, we give an analyzing example for proving the accuracy and validity of this uncertainty measurement for covering rough-vague set.