The incremental method for fast computing the rough fuzzy approximations

The lower and upper approximations are basic concepts in rough fuzzy set theory. The effective computation of approximations is very important for improving the performance of related algorithms. This paper proposed and proved two incremental methods for fast computing the rough fuzzy approximations, one starts from the boundary set, the other is based on the cut sets of a fuzzy set. Then some illustrative examples are conducted. Consequently, two algorithms corresponding to the two incremental methods are put forward respectively. In order to test the efficiency of algorithms, some experiments are made on a large soybean data set from UCI. The experimental results show that the two incremental methods effectively reduce the computing time in comparison with the traditional non-incremental method [1].