差别矩阵约简表示及其快速算法实现

Discernibility matrix-based reduct representation and quick algorithms

差别矩阵可以拥有不同的信息,根据差别矩阵描述的区分信息量不同,给出4种差别矩阵定义,并提出相应H-约简、S-约简、B-约简和P-约简的概念;研究4种约简之间的关系,构建通用约简算法模型.为了提高约简算法的效率,给出相对分辨能力约简定义(RD-约简),揭示相对分辨能力约简与4种差别矩阵约简之间的等价性,进而设计相对分辨能力快速约简算法.最后,通过实例和UCI数据集验证了所提出约简算法的有效性和时空性能.

The discernibility matrix can possess different information. In this paper, according to different discernible information quantity, four descriptions of the discernibility matrix are proposed, and the four reduct definitions, i.e., Hreduct, S-reduct, B-reduct and P-reduct are presented. The relationship and equivalence for four reducts are researched,and two general reduction algorithms are designed. In order to improve the efficiency of the reduction algorithm, the related concepts of the relative discernibility-based reduct（denoted as RD-reduct） are proposed. The equivalence between the relative discernibility-based reduct and four discernibility matrix-based reducts are revealed. Two effective reduction algorithms based on the relative discernibility are designed. Finally, the example and experiments are used to explain the feasibility and effectiveness of the proposed algorithms.