This artical will use the similar way as [ 1 ] by the discussion to many kinds of situations and by the calculation to the codimention of ideal to discuss the classification and of differential function germs whose codimention is more than 5 and less than or equal to 8 本文将使用与论文类似的方法，经过对各种情况的讨论和理想的余维数计算，对余维数大于5小于等于8的可微函数芽的分类加以讨论，并给出证明。
The basic rough set theory is introduced in brief . the method of how to get the decision rules through the rough set and recent popular arithmetic methods are mentioned . finally , a real - life example is given to explain the basic notions and get the decision rules to illustration the problem 3 .引入非参数式可变精度粗糙集模型,介绍一些基本的概念和性质,并给出证明;用分布一致性方法来对多属性决策问题进行多属性约简,引入相关的概念,并对所得到的性质和判定定理,给予理论上的证明,得出最后的决策步骤,并且最终获得多属性决策问题的决策规则。
