Dynamic maintenance of approximations under fuzzy rough sets

The lower and upper approximations are basic concepts in rough set theory. Approximations of a concept in rough set theory need to be updated for dynamic data mining and related tasks. Most existing incremental methods are based on the classical rough set model and limited to describing crisp concepts. This paper presents two new dynamic methods for incrementally updating the approximations of a concept under fuzzy rough sets to describe fuzzy concepts, one starts from the boundary set, the other is based on the cut sets of a fuzzy set. Some illustrative examples are conducted. Then two algorithms corresponding to the two incremental methods are put forward respectively. The experimental results show that the two incremental methods effectively reduce the computing time in comparison with the traditional non-incremental method.