利用关联矩阵探究属性约简方法

Using Association Matrix to Explore Attribute Reduction

形式背景的属性约简可以约简掉不必要的属性,使得其结构变得简单,一定程度上降低规则提取的难度.利用图论中有向图的性质并结合关联矩阵,对形式背景的属性约简问题进行考虑,找出所给形式背景中两两属性之间覆盖关系生成有向边,再利用有向图中弧的头与尾的性质,找到生成边与属性之间的对应关系,并用关联矩阵表示出来,进而可以得到一个关于属性与属性之间生成有向边的表格,之后对表格中每一行构成情况进行分析,根据属性特征覆盖关系以及有向图中弧之头与尾的性质,给出了不必要属性的判别定理,根据不必要属性的判别定理可以推得核心属性的判别,根据此给出完成属性约简的算法,并通过实例验证算法的可行性.

The attribute reduction for a formal context can reduce unnecessary attributes in order to make the structure of the formal context be simple. According to this way,the difficulty of rule extraction from the formal context becomes low er. Combining the correlation matrices with the properties of a directed graph in graph theory,the attribute reduction problem of a formal context is considered. As a result,the coverage relationship between any two of attributes in the given form context is found so that to generate the directed edges. Furthermore,applying some properties for the head and tail for arcs in a directed graph in finding the correspondence between the generated edges and the attributes,the correspondence relationship is represented by a correlation matrix. Hence,a table can be obtained for generating the directed edges between any of the attributes and any of the other attributes. After that,the composition of each line in the table is analyzed. According to the coverage relationship among attributes and the properties of the head and tail of an arc in the directed graph,a judgement theorem for unnecessary attributes is proposed. According to the judgement theorem of unnecessary attributes,the core attribute can be deduced. Based on those theorems,an algorithm of attribute reduction is given. The feasibility of the algorithm is verified by an example.