Attribute reduction in inconsistent formal decision contexts based on congruence relations

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• 作者：Jun-Yu Li ; Xia Wang ; Wei-Zhi Wu ; You-Hong Xu
• 关键词：Inconsistent formal decision context ; Attribute reduction ; Congruence relation ; Rough set ; Three ; way concept analysis
• 刊名：International Journal of Machine Learning and Cybernetics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：8
• 期：1
• 页码：81-94
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Computational Intelligence; Artificial Intelligence (incl. Robotics); Control, Robotics, Mechatronics; Complex Systems; Systems Biology; Pattern Recognition;
• 出版者：Springer Berlin Heidelberg
• ISSN：1868-808X
• 卷排序：8

文摘

In this paper, notions and methods of attribute reduction are investigated for an inconsistent formal decision context. Based on congruence relations defined on the object power set, we first introduce notions of distribution attribute reduct and maximum distribution attribute reduct for an inconsistent formal decision context, and discuss their relations in detail. We then define discernibility matrices and discernibility functions associated with the proposed attribute reducts, from which we can calculate all attribute reducts. Finally, we compare the proposed consistent sets with four types of consistent sets in previously published papers. The results show that a distribution consistent set belongs to any of those four types of consistent sets. Therefore, it has all the properties of those four types of consistent sets.