区间值序信息系统中差别信息树的属性约简

Attribute Reduction of Discernibility Information Tree in Interval-Valued Ordered Information System

属性约简是粗糙集领域的一个热门研究课题,而差别矩阵是获得属性约简的有效方法。然而,差别矩阵含有重复元素,增加了获得约简所需要的时间。差别信息树的提出解决了差别矩阵含有重复元素的问题,实现了对差别矩阵中非空元素的压缩存储。但是差别信息树是在等价关系下的差别矩阵的基础上提出的,并没有考虑序决策信息系统的情况。在区间值序信息系统的背景下提出了基于可分辨矩阵的差别信息树,解决了可分辨矩阵中存在冗余元素的问题,实现了对可分辨矩阵中非空元素的压缩存储。得到了该树的相关性质定理并对其进行了验证,并在此基础上给出区间值序信息系统的基于差别信息树的完备的属性约简方法。最后给出了实证分析,验证了该方法的可行性以及有效性。

Attribute reduction is a hot topic in rough set, and discernibility matrix is an effective method to get attribute reduction. However, the discernibility matrix contains duplicate elements, which increases the time needed to get the reduction. The discernibility information tree solves the issue, and realizes the compression storage of the non-empty elements in the discernibility matrix. Unfortunately, the discernibility information tree is based on the discernibility matrix under the equivalence relation, and does not consider the situation of the ordered decision information system. In this paper, a discernibility information tree is proposed based on distinguishable matrix in interval-valued ordered information systems, which solves the problem of redundant elements in the distinguishable matrix and realizes the compression storage of non-empty elements in the distinguishable matrix. Furthermore, the related theorem of the tree is obtained and verified carefully. And, a complete attribute reduction method is given based on the discernibility information tree of the interval-valued ordered information system. Finally, an empirical analysis is addressed, which verifies the feasibility and effectiveness of the method.