基于面向对象(属性)概念格的三支规则提取

Three⁃way rules acquisition based on object(attribute)⁃oriented concept lattices

三支形式概念分析作为形式概念分析的推广,从正信息和负信息角度对概念进行了更精细和更完整的描述.针对决策形式背景,从三支决策思想的视角研究对象导出三支面向对象概念格(OEO-概念格,Object-induced three-way object-oriented)和属性导出三支面向属性概念格(AEP-概念格,Attribute-induced three-way property-oriented)的规则提取问题.首先,借助三支算子给出OEO-协调以及对象导出面向对象三支决策规则的概念,在此基础上研究其规则与面向对象概念格的决策规则之间的关系,研究结果显示当决策形式背景在OEO-协调和面向对象协调的前提下,两者之间存在包含关系.其次,对偶地,提出AEP-协调和属性导出面向属性三支决策规则的定义,并讨论其与面向属性概念格的决策规则之间的关系,进一步地刻画其与属性导出三支决策规则之间的联系.最后,结合实例详细解释所提出的理论.

As a generalization of formal concept analysis,three-way formal concept analysis describes more precisely and completely concepts from the perspective of positive information and negative information.Based on formal decision contexts,this paper discusses the rules acquisition of object-induced three-way object-oriented concept lattice(OEO-concept lattice,Object-induced three-way object-oriented)and attribute-induced three-way property-oriented concept lattice(AEP-concept lattice,Attribute-induced three-way property-oriented)by three-way decision.Firstly,the notions of OEO-consistence and object-induced object-oriented three-way decision rule are investigated.On this basis,the relationship between three-way decision rule and decision rule of object-oriented concept lattice is discussed.The result shows that there is an inclusive relation under the premise of OEO-consistent and object-oriented consistent formal decision context.Furthermore,in duality,the definitions of AEP-consistence and attribute-induced attribute-oriented three-way decision rule are illustrated.And the relations among them,decision rule of property-oriented concept lattice and property-induced three-way decision rule are described.Finally,examples are conducted to illustrate the proposed theory.