A Method for Incremental Updating Approximations when Objects and Attributes Vary with Time

The description of an information system will be more accurate when objects and attributes are added to it. The approximations of a concept may change when an information system varies. No research work has been done yet on incremental updating for approximations when objects and attributes change simultaneously. In traditional rough set theory, granules are induced by equivalence classes. The granularity of an information system may become smaller when attributes are added. New granules may be generated or the granularities of some existing granules may become larger when objects are inserted. There will be complex changes of granularity of an information system when objects and attributes are added simultaneously. Firstly, the composition and decomposition of granules are analyzed. Then an algorithm for incremental updating approximations is proposed. Finally, an illustrative example is given to validate the method for incremental updating approximations.