基于粒计算的变形分明函数分析及属性约简证明

为了对分明矩阵和分明函数属性约简法予以理论上的证明,一个变型的分明函数被构造,它被定义为析取范式的逻辑公式.通过对变型分明函数以及等价转换成的最简式对应粒性质的讨论,证明了变型分明函数对应的粒等于所有分明关系的并.由此证明了最简式中所有的合取项就是信息系统属性集的全部约简.从而以粒计算的方法完成了分明矩阵和分明函数属性约简法的理论证明.

Analysis on new discernibility function and proof about attribute reduction based on granular computing

In order to make a proof for the attribute reduction completed by the discernibility matrix and function, a new discernibility function which is defined as a disjunctive normal form is constructed. By investigating granules corresponding to the new discernibility function, as well as to the most succinct formula which is transformed from the new discernibility function, it is concluded that the granule corresponding to the new discernibility function is equal to the union of all discernibility relations. Consequently, it proves that all conjunctive items of the most succinct formula are all reductions of the attribute set in the information system. So, based on granular computing, the theoretical proof for the attribute reduction determined by the discernibility matrix and function is completed.