基于信息熵的形式背景属性约简

Attribute Reductions of Formal Context Based on Information Entropy

属性重要度和属性约简都是形式概念分析研究中的关注重点.通过信息粒的角度,文中提出基于信息熵研究形式背景的属性约简的一些方法.首先,给出形式背景的信息熵、条件熵及互信息等定义,通过条件熵对协调的决策形式背景进行属性约简,得到形式背景的粒协调和熵协调是等价的.然后,在熵不协调的决策形式背景中定义有限信息熵、有限条件熵和有限互信息,利用有限条件熵对不协调的决策形式背景进行属性约简.最后,基于属性重要度分别设计熵协调和熵不协调的决策形式背景的属性约简算法,通过数值实验验证文中算法的有效性.

Attribute significances and attribute reduction are crucial in formal concept analysis.Some approaches to attribute reduction of formal context are proposed based on information entropy.Firstly,information entropy,conditional entropy and mutual information of formal context are defined,and attribute reduction by means of conditional entropy is conducted in consistent decision formal context.The equivalence between the granular consistency and the entropy consistency in decision formal context is produced.Secondly,limitary information entropy,limitary conditional entropy and limitary mutual information are proposed,and attribute reductions are conducted by means of limitary conditional entropy in inconsistent formal decision context.Finally,the attribute reduction algorithms of consistent and inconsistent formal decision contexts are proposed by the significance of attributes,and numerical experiments show the efficiency of the proposed algorithms.