Abstract: One direction singular rough sets and the structure of dual of one direction singular rough sets were given.One direction singular rough sets and dual of one direction singular rough sets come from improved Z. Pawlak rough sets. One direction singular rough sets and dual of one direction singular rough sets have dynamic characteristics. The relation between one direction singular rough sets, dual of one direction singular rough sets and Z. Pawlak rough sets was also proposed.S-rough sets have three types of forms: one direction singular rough sets, dual of one direction singular rough sets and two directions singular rough sets. Based on one direction singular rough sets, dual of one direction singular rough sets, the concepts of data internal-mining, data outer-mining and their Outer concentric circle theorem,Internal concentric circle theorem were proposed, and the applications were given. S-rough sets is a new branch of Rough sets theory and applied research.

Key words: One direction singular rough sets, Dual of one direction singular rough sets, Data internal-mining, Data out er-mining, Unit circle, Outer concentric circle theorem, Internal concentric circle theorem, Application