基于形式背景的概念格约简及其修复

Concept Lattice Reduction and Reparation Based on Formal Context

根据概念格构造所依赖的形式背景,定义对象的属性空间和属性的对象空间,分别对形式背景进行对象约简和属性约简,在约简过程中采取全约简、交约简和并约简3种约简方法,并基于约简形式背景建立约简概念格。针对各约简方法的不同提出约简概念格的不同修复方法,从而得到完整的概念格。该方法简单易行,具有很强的规则性。实例表明,对于一个较复杂的形式背景,按对象和属性总数的38%进行约简,运算效率可提高83.3%。

According to the formal context which the construction of concept lattice depends on, this paper gives the definitions of attribute spaces of object and object spaces of attribute, and adopts the objects reduction and attributes reduction in formal context. In the process of reduction, three reduced methods are presented, atld based on the reduced formal context, the reduced concept lattice is constructed. A complete concept lattice is to be obtained through the different reparation methods. The method has the characteristics of regularization and simplification. Example expresses that reducing the object and attribute at the rate of 38% for a more complex formal context, the operation efficiency can raise 83.3%.