计算机应用 ›› 2019, Vol. 39 ›› Issue (10): 2852-2858.DOI: 10.11772/j.issn.1001-9081.2019030438

• 人工智能 • 上一篇    下一篇

关系决策系统中相对不可区分和区分关系的约简

李旭, 荣梓景, 阮晓曦   

  1. 北京语言大学 信息科学学院, 北京 100083
  • 收稿日期:2019-03-18 修回日期:2019-05-14 发布日期:2019-05-27 出版日期:2019-10-10
  • 通讯作者: 李旭
  • 作者简介:李旭(1986-),男,新疆乌鲁木齐人,博士研究生,主要研究方向:粗糙集、属性约简;荣梓景(1995-),男,山西晋城人,硕士研究生,主要研究方向:粗糙集、属性约简;阮晓曦(1986-),女,北京人,博士研究生,主要研究方向:粗糙集、属性约简。

Attribute reduction of relative indiscernibility relation and discernibility relation in relation decision system

LI Xu, RONG Zijing, RUAN Xiaoxi   

  1. School of Information Science, Beijing Language and Culture University, Beijing 100083, China
  • Received:2019-03-18 Revised:2019-05-14 Online:2019-05-27 Published:2019-10-10

摘要: 针对相对不可区分和区分关系约简的问题提出相应的算法。首先,考虑等价关系中相对不可区分关系的约简,提出一种新的辨识矩阵,并在此基础上得到了一种约简算法,通过关系的补关系提出相对区分关系的约简算法。然后,将相对不可区分关系等概念推广到一般关系。对于关系决策系统的相对不可区分关系约简给出了相应的辨识矩阵,并利用关系的补关系得到了相对区分关系约简的辨识矩阵,从而得到了两者的约简算法。最后,在选取的UCI数据集上,对提出的算法进行验证。在等价关系上,基于绝对约简的相对不可区分关系的约简(EQIND)算法与相对不可区分一般关系的约简(BⅡND)算法所得约简相同,基于绝对约简的相对区分关系的约简(EQDIS)算法与相对区分一般关系的约简(BIDIS)算法所得约简相同;同时算法BⅡND、BIDIS可以对不完备决策表进行约简。实验结果验证了所提算法的可行性。

关键词: 粗糙集, 不可区分关系, 区分关系, 关系决策系统, 属性约简

Abstract: Corresponding reduction algorithms for relative indiscernibility and discernibility relation were proposed. Firstly, considering the reduction of the relative indiscernibility relation in equivalence relation, the corresponding discernibility matrix was proposed and a reduction algorithm was proposed based on the matrix. Then, a reduction algorithm for relative discernibility relation was proposed according to the complementary relationship of the relation. Secondly, the concepts such as relative indiscernibility relation were expanded to the general relation. The corresponding discernibility matrix was proposed for the relative indiscernibility relation reduction in the relation decision system, and the corresponding discernibility matrix for the relative discernibility relation reduction was obtained by using the complementary relationship of the relation, so the reduction algorithms for both relations were obtained. Finally, the proposed algorithms were verified on the selected UCI datasets. In the equivalence relation, the algorithm of the relative EQuivalence INDiscernibility relation reduction based on absolute reduction (EQIND) and the algorithm of the relative BInary INDiscernibility relation reduction (BⅡND) have the same results. The algorithm of the relative EQuivalence DIScernibility relation reduction based on absolute reduction (EQDIS) and the algorithm of the relative BInary DIScernibility relation reduction (BIDIS) have the same results. Meanwhile, BⅡND and BIDIS are suitable for the incomplete decision table. The feasibility of the proposed algorithms were verified by the experimental results.

Key words: rough set, indiscernibility relation, discernibility relation, relation decision system, attribute reduction

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