Abstract:

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.

Key words: attribute reduction, Boolean matrix, heuristic algorithm, object-induced three-way concept lattice

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。

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