摘要
不完备决策系统关联于数据分析,其属性约简具有应用意义,并已具有基于容差关系的条件熵研究.基于相似关系,研究不完备决策系统的条件熵属性约简及其算法.利用相似关系确立条件熵,提出等价于广义决策函数保持约简的条件熵保持约简,建立具有误差容忍机制的条件熵容忍约简;针对两种新建属性约简,揭示它们间的扩张关系与强弱关系,构建相应的全局算法与局部算法;最后,提供决策表实例分析,说明基于相似关系的条件熵属性约简及其算法的有效性.相关研究完善了不完备决策系统属性约简,具有理论价值与应用意义.
The incomplete decision system is related to data analyses;its attribute reduction has application significance, and already exists conditional entropy research based on tolerance relations. Based on similarity relations, the conditional entropy reduction and its algorithms are investigated in the incomplete decision system. Firstly, the similarity relation is used to establish the conditional entropy, the attribute reduction regarding the conditional entropy preservation is proposed to be equivalent to the reduction regarding the generalized decision function preservation, and the attribute reduction regarding the conditional entropy tolerance is developed to have the fault tolerance mechanism. According to the two new types of attribute reduction, their extended and strong-weak relationships are then revealed, and the global and local algorithms are correspondingly constructed for calculation. Finally, a decision table is provided for example analyses, and the effectiveness of conditional entropy reduction and its algorithms are illustrated based on similarity relations. The relevant study completes the attribute reduction of incomplete decision system, thus holding the theory value and application significance.
作者
黄宜纯
杨霁琳
张贤勇
莫智文
HUANG Yi-chun;YANG Ji-lin;ZHANG Xian-yong;MO Zhi-wen(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,China;Key Lab of Cloud Computing and Intelligent Information Processing,Sichuan Technology and Business University,Chengdu 611745,China;Institute of Intelligent Information and Quantum Information,Sichuan Normal University,Chengdu 610066, China)
出处
《数学的实践与认识》
北大核心
2019年第2期166-175,共10页
Mathematics in Practice and Theory
基金
国家自然科学基金(61673285
11671284
61203285)
四川省科技支撑计划(2017JY0197)
四川省青年基金项目(2017JQ0046)
四川省教育厅科研项目(2017JQ0046)
关键词
粗糙集
不完备决策系统
属性约简
容忍约简
条件熵
相似关系
rough set
incomplete decision system
attribute reduction
tolerance reduction
conditional entropy
similarity relation
