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.