Double-local conditional probability based fast calculation method for approximation regions of local rough sets

As an important extension of classical rough sets, local rough set model can effectively process data with noise. How to effectively calculate three approximation regions, namely positive region, negative region and boundary region, is a crucial issue of local rough sets. Existing calculation methods for approximation regions are based on conditional probability, the time complexity is O(|X||U||C|). In order to improve the computational efficiency of three approximation regions of local rough sets, we propose a double-local conditional probability based fast calculation method. First, to improve the computational efficiency of equivalence class, we define the double-local equivalence class. Second, based on the doublelocal equivalence class, we define the double-local conditional probability. Finally, given the probability thresholds and a local equivalence class, the monotonicity of double-local conditional probability is proved, on this basis, a double-local conditional probability based fast calculation method for approximation regions of local rough sets is proposed, and the time complexity is O ( MAX ( |X|(2)|C|, |X| broken vertical bar X-C broken vertical bar |C|)). Experimental results based on 9 datasets from UCI demonstrate the effectiveness of the proposed method.