不完备信息系统下的一种概率属性约简算法

Probability Algorism for Attributes Reduction in Incomplete Information System

不完备信息系统中的属性约简一直是粗糙集研究领域的一个难点.在不完备信息系统中,用以往的属性约简算法得到的约简结果中,某一属性要么属于该约简,要么不属于该约简.但在实际生活中,当属性以比较大的概率可区分两对象时,这就表明该属性可能以某一概率属于约简结果.基于这种想法,文中通过构造概率区分矩阵,并在此基础上给出相应的区分函数,提出了一种概率属性约简算法,分析了算法正确性.从该算法得到的约简,可以看出各属性属于约简的可能性.最后用实例表明该算法是有效和可行的.

Attributes reduction based on rough set theory is an important but difficult task under incomplete information system. For the attributes reduction which is gained by the old attributes reduction algorisms , the attribute belongs to it or not . Nevertheless in the practice when there is the probability that the attribute can discern two objects , this shows the attribute may belong to the attribute reduction. Probability discernibility matrix is defined and corresponding discernibility function is given. Then a probability algorism for attributes reduction is proposed and an example shows the algorism is effective. The probability that the attribute belong to the reduction can be know from the reduction which is gained by the algorism.