中文摘要：

约筒是知识获取的重要方法之一，基于等价关系的粗糙集约筒理论的研究已比较深入，而优势关系下约简理论的研究还比较少。定义了模糊目标信息系统在优势关系下的5种属性约筒，并且给出了它们的判定定理和可辨识矩阵。证明了辨识矩阵对应的辨识公式给出的解就是所求约筒的全体．最后通过一个例子说明如何用辨识矩阵算法求属性约简。

英文摘要：

Knowledge reduction based on rough set theory is one of the important methods of knowledge -acquisition. Comparatively speaking, the attribute reduction based on equivalence relation has been investigated in depth, however, there is less study of attribute reduction based on dominance relation, so, in the paper five kinds of knowledge reduction are defined. The judgment theorems and discernibility matrixes with respect to these reductions are established, from which the algorithms of discermibility matrix for finding these reductions are obtained. Finally, an example is given.