基于相似关系的不完备形式背景属性约简

Attribute reduction of incomplete contexts based on similarity relations

研究不完备形式背景的属性约简问题。通过比较对象间属性值的一致性,定义了对象集上的一个相似关系,进而定义了基于相似关系的粗糙近似算子,利用目标集的粗糙集近似,可以提取语义明确的决策规则。基于不完备形式背景中相似关系给出一种属性约简的概念,研究了属性约简的判定定理,给出了三类属性的特征刻画。最后,利用对象间的辨识属性,给出了一种属性约简的方法,并举例说明了方法的可行性。

The paper focuses on the attribute reduction of incomplete contexts. First,by comparing the values of the objects on each of the attributes,one kind of similarity relations is proposed in incomplete contexts,based on which decision rules with clear meaning can be revealed via rough approximation operators. Subsequently,one type of attribute reduction of incomplete contexts is defined,under which the similarity relations keep unchanged,some judgment theorems are given for attribute reduction,and different types of attributes for attribute reduction are characterized by the similarity relations. At last,by constructing a Boolean function with discernibility attributes among objects,an approach for attribute reduction is obtained,and an illustration example is taken to show the reliability of approach.