基于形式背景转化的概念格属性约简

Attribute Reduction of Concept Lattice Based on Transformation of Formal Context

借鉴形式背景下概念格的经典属性约简,立足决策形式背景,通过转换提出一种新的概念格属性约简,其对一般约简具有结构诱导性。首先,在决策形式背景下定义一致集,提出概念格的一致属性约简及对应算法,得到一致属性约简与三分属性的关系。其次,研究新建的一致约简与已有的强一致约简和弱一致约简之间的关系,得到一致约简具有关于概念格属性约简的严格强性,并由此设计由强至弱的启发式约简算法。最后,给出具体实例,说明与验证相关的约简、性质和算法。

By referring to the classical attribute reduction of concept lattice in formal context,a new attribute reduction of concept lattice in decision formal context was proposed by transformation,and it had structural induction for general reducts.Firstly,consistent sets were defined in decision formal context,and consistent reducts and their algorithms were proposed for concept lattice.Moreover,connections between consistent attribute reducts and three-way attributes were acquired.Secondly,relationships of consistent reducts regarding existing strong-consistent reducts and weak-consistent reducts were investigated,thus,consistent reducts exhibited the strict strength in terms of attribute reduction of concept lattice,and heuristic reduction algorithms from the strong to the weak were designed.Finally,the relevant reducts,properties and algorithms were illustrated and validated by detailed examples.