Studies On The Covering Rough Set Theory And Application

In order to deal with the knowledge of inharmonious, incomplete, anduncertainty. Rough set concepts and theory were proposed by Poland scholar Pawlakin1982, which provides a new method to deal with uncertain problems byequivalence relation. To deal with problem of more widely, Zakowski extendsdivision to covering and promotes the classical rough set theory to generalizedcovering rough set theory.In this paper two kinds of covering rough sets were studied based ongeneralized covering rough set. The main research results and innovations asfollows:First, the upper and lower approximations of a covering rough set based on theprobability are studied in this paper, and its properties, digital features, topologicalfeatures are given, which provides a new model for the study of covering rough set.Second, the definition of the upper and lower approximations of the coveringrough set based on the close friend element are defined, moreover the properties arediscussed. The matrix description of the covering rough set based on the close friendelement are given, which gives a new way to get the upper and lower approximationsof rough set definitions depict a new way.Third, the method based on close friend element of grain and family reductionalgorithm of covering rough set is given, and an application example is given.In this paper, through introducing the covering rough set based on close friendelement, a method to solve the reduction of information system are given, whichenrich the research contents of the covering rough set.