Knowledge Distance Measure for the Multigranularity Rough Approximations of a Fuzzy Concept

Different rough approximation spaces could be induced for an information system by its different attribute subsets, thus the multigranularity rough approximations of a fuzzy concept could be developed. Research on the uncertainty in multi-granulation spaces becomes a basic issue of uncertainty measure. If the uncertainty measure is not accurate enough, two different rough approximation spaces of a fuzzy concept may have the same uncertainty, and the difference between them for describing a fuzzy concept cannot be reflected. In this case, attribute reduction, granularity selection, and multigranularity measure cannot be conducted effectively. Therefore, establishing an uncertainty measure model with strong distinguishing ability in multi-granulation spaces is a key issue in uncertainty knowledge processing. In this paper, this problem will be solved in the view of knowledge distance. First, a fuzzy knowledge distance measure (FKD) based on the Earth Mover's distance is introduced. Even if two rough approximation spaces possess the same uncertainty when describing a fuzzy concept, they can be discriminated by FKD. Then, by studying the change rules of the FKD in a hierarchical quotient space structure, it is found that the FKD between any two rough approximation spaces in an HQSS is equal to the difference between their granularity measure or information measure. Furthermore, in order to show the applicability of the FKD, the FKD is used in granularity selection, attribute reduct, and multigranularity measure. The experimental results show that the FKD-based attribute significance function has a more powerful ability to obtain shorter reduct and it is more robustness, which show the effectiveness of the FKD.