The Theory And Reduction Algorithm Of Multigranulation Covering Rough Set

Pawlak rough set, a new mathematical tool dealing with vagueness and uncertainty, isbased on equivalence relation. However, the rough set can not deal with the situation in whichthe intersection operation is not established amongs granulations. So the multigranulationrough set is proposed by Qian Yuhua based on equivalence relation and similar relation. ButQian’s multigranulation rough set also has its limitations when the object is comparative andnumerical data or continuous data. So in this paper, the multigranulation rough set based ondominance relation and the multigranulation covering rough set theory and its reductionalgorithm are presented as follows:(1) The multigranulation rough set is proposed which is based on dominance relation,and the mutilgranulation approximate upper and lower are defined, some properties andconclusions based on multigranulation are characted. An example is given to illustrate thedifferences between singlegranulation and multigranulation rough set.(2) The mutilgranulation covering rough set is proposed. The upper and lowerapproximate are defined in the sense of multigranulation. Some properties and conclusionsbased on multigranulation are characted.(3) The attribute reduction algorithm of mutilgranulation covering decision rough set isproposed, and it is analysised by using example.