To Compare the Theory of Quotient Space with Rough Set

The relationship between rough set and quotient space is discussed by comparing in the paper.After analyzing basic algorithms and complexity and expansibility in theory about rough set and quotient space,think that the same point of them is to represent granule by using equivalence relation and to depict concept by using granule.But the emphasis of both discussions is difference.The theory of quotient space researches transformed and depended relations between different granules mainly.It is the theory to represent space relationship.For granular computing today such as rough set,it studies to represent and depict granule and relation between granule and concept primarily.The greatest difference is that there is topological relation among domain elements in the theory of quotient space,i.e.the domain is a topological space.Whereas the domain of rough set is only simple point set,there is no topological relation among elements.So the theory of quotient space applies to not only data mining and knowledge discovery,but also restriction problem such as route layout and space state distributing etc.