A Fuzzy Rough Set Approach for Incrementally Updating Approximations in Hybrid Information Systems

In real-applications, there may exist missing data and many kinds of data e.g., categorical, real-valued and set-valued data in an information system which is called as a Hybrid Information System HIS. A new Hybrid Distance HD between two objects in HIS is developed based on the value difference metric. Then, a novel fuzzy rough set is constructed by using the HD distance and the Gaussian kernel. In addition, the information systems often vary with time. How to use the previous knowledge to update approximations in fuzzy rough sets is a key step for its applications on hybrid data. The fuzzy information granulation methods based on the HD distance are proposed. Furthermore, the principles of updating approximations in HIS under the variation of the attribute set are discussed. A fuzzy rough set approach for incrementally updating approximations is then presented. Some examples are employed to illustrate the proposed methods.