The Dominant-Recessive Characteristics and Hiding-Mining

This paper presents the concepts of ladder information (which is called ladder knowledge) and a pair of \(\left(F,\overline{F }\right)\)-ladder degree, by employing one direction singular rough sets and dual of one direction singular rough sets as well as their dynamic characteristics. The discernibility theorem of \(\left(F,\overline{F }\right)\)-ladder information, the mining-discovery theorem, the hiding-discovery theorem, the mining-discovery theorem of maximum, the hiding-discovery theorem of maximum and the dependence-filter theorem of knowledge mining-discovery are proposed, and the recessive characteristics discovery principle of \(\left(F,\overline{F }\right)\)-ladder information, the hiding-discovery criterion of ladder information are given with ladder information and ladder coefficient concepts. The results given in this paper show the new characteristics and the new applications of the dynamic characteristic of one direction singular rough sets and dual of one direction singular rough sets. In particular, \(\left(F,\overline{F }\right)\)-ladder information has an important application in big data intelligent separation-acquisition.