Generalizing quotient space theory from structural viewpoint

Quotient space theory of problem solving, a formal model of granular computing, is generalized in the sense that topological structure is replaced by Cech's closure space. Some basic issues of granular computing, such as the representation of real world at different levels of granularity, property preserving and the construction of granular world, are discussed in detail. It turns out that most of conclusions of the classical quotient space theory keep being valid, so intension and applicable fields are enriched and enlarged respectively.