基于OE-概念格的形式背景属性约简  

Attribute Reduction in Formal Contexts Based on OE-Concept Lattices

作　　者：张呈玲 李进金 林艺东 ZHANG Chengling;LI Jinjin;LIN Yidong(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China;School of Mathematical Sciences,Xiamen University,Xiamen,Fujian 361000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]厦门大学数学科学学院,福建厦门361000

出　　处：《计算机工程与应用》2021年第15期82-89,共8页Computer Engineering and Applications

基　　金：国家自然科学基金(11871259,61379021,11701258);福建省自然科学基金(2019J01748,2017J01507)。

摘　　要：在三支概念格的属性约简框架下,借助布尔矩阵理论,研究保持OE-对象粒矩阵不变的属性约简问题。给出OE-对象粒矩阵的概念以及OEG粒协调集的定义,在此基础之上讨论属性之间的相似性,并且刻画属性的内外重要度。针对对象导出三支概念格的形式背景设计基于矩阵理论的启发式属性约简算法。将上述理论结果应用于对象导出三支概念格的决策形式背景,提出三支协调决策形式背景及OEG粒协调集的概念,并且从规则提取的角度说明约简集对应的OE-概念格的决策形式背景的三支规则集比原背景的三支规则集更加简洁。通过数值实验阐明该理论的可行性和合理性。In the framework of attribute reduction of three-way concept lattices,this paper studies the attribute reduction by keeping OE-object granular matrix based on Boolean matrix theory.Concepts of OE-object granular matrix and OEG granular consistent set are defined.On this basis,this paper discusses the internal and external significance measure of attribute according to the similarity degree.A heuristic approach of attribute reduction based on matrix theory in formal context based on object-induced three-way concept lattice is designed.Furthermore,the above theoretical result is applied to the decision formal context based on object-induced three-way concept lattice,and provides the definitions of three-way consistent decision formal context and OEG granular consistent set.The rule set of decision formal context based on OE-concept lattice corresponding to the reduct is more concise than that of original context from the perspectives of decision rule.The numerical experiment illustrates that the above theory is practicable and reasonable.

关 键 词：属性约简 布尔矩阵 启发式算法 对象导出三支概念格 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]