F?-ladder knowledge and F?-hiding knowledge discovery

By employing dual of one direction S-rough sets (dual of one direction singular rough sets) and its dynamic characteristic, this paper presents the concepts of F̅-ladder knowledge and F̅-ladder degree. Using these concepts, the discernibility theorem of F̅-ladder knowledge, the hiding-discovery theorem of maximum F̅-ladder knowledge, the hiding-discovery theorem of maximum F̅-ladder knowledge and the dependence-filter theorem of knowledge discovery are proposed, and the interior hiding principle of F̅-ladder knowledge, the hiding-discovery criterion of F̅-ladder knowledge and its applications are given. The results given in this paper show the new characteristics of dual of one direction S-rough sets and the new applications of the dynamic characteristic of dual of one direction S-rough sets.