Research in Quotient Space Theory Based on Structure

The quotient space theory is indented to study the relationship of transform and that of dependency among the worlds with different grain-size. Compared with other granule computing tools, it has more powerful abilities of representation and absorption. The reason is that structure is introduced in its model. The paper is to study the quotient space theory based on structure. We first introduce some methods of constructing quotient structure. Then we study in detail the quotient space family based on structure, and get some good results for further research. Finally we also briefly discuss hierarchical structure of fuzzy sets