Abstract The theory of quotient space is one of the three main methods of granular computing. The research of its combination is to find the relationship between the quotient space and the original space and to reduce the computational complexity by simplifying complex problems. The combination of domains is intended to implement granularity transform, fine or coarse, according to the different needs. The topological structure is the unique structure in the quotient space theory, and its combination has a variety of forms. In addition to the fine combination and the semi-order structure combination, the coarse combination and the converse quotient combination based on the converse-quotient topology are presented. The combination reflects the relationship between different topological structures. The combination of attribute functions lies in the formation of different equivalence relation of domain. These studies extend the basic theory of quotient space combination and make it better.
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2013, Vol. 26 
