不完备信息系统属性约简的矩阵算法

Matrix Algorithm for Attribute Reduction in Incomplete Information System

通过分析不完备信息系统中基于相容矩阵的属性约简算法,定义一个在单个条件属性下的新二进制相容矩阵,给出新矩阵间的吸收运算规则,利用该规则得到不完备信息系统条件属性集的二进制相容矩阵。通过判断新二进制相容矩阵间运算后得到的矩阵是否与条件属性集下的矩阵等价,找出不完备信息系统的属性约简。证明该属性约简与不完备信息系统中基于正区域的属性约简是等价的,并给出属性约简算法。实例证明该算法是合理的。

By analyzing attribute reduction based on tolerance matrix in incomplete information system,a new binary tolerance matrix under single condition attribute is defined.At the same time,absorption of operation rule between two of them is also defined.The binary tolerance matrix under the whole condition attributes is gained by that rule.If the binary tolerance matrix based on some of condition attributes is equal to the binary tolerance matrix under the whole condition attributes,those condition attributes make up of an attribute reduction.It is proved that the attribute reduction acquired from this new method is equivalent to it based on positive region in incomplete information system,and an algorithm for attribute reduction is presented.An example is used to illustrate the rationality of this new algorithm.