Abstract: Rough set theory is a new mathematical tool to deal with vagueness and uncertainty. The classical rough set theory based on equivalence relation has made a great progress, while the equivalence relation is too harsh to meet and is extended to tolerance relation in real world. It is important to investigate rough computational methods for rough set theory, which is one of the bottleneck problems in the development of rough set theory. Matrix computation based on tolerance relation for information systems is discussed, and a one-to-one relationship between tolerance relation and tolerance matrix is constructed in this paper. Two algorithms for attribute reduction in incomplete information system are presented with an example to illustrate their validity.