关键词: 商空间, 饱和集, 逆商空间, 一致性

Abstract: Granular computing is a new method to simulate human thinking and solve complex problems in the field of computational intelligence. Quotient space theory is one of the three main methods of granular computing. On the basis of the theory of quotient space, the correlation property of the inverse quotient space is analyzed, and the consistency between the quotient space and the original space is analyzed. It is proven that the inverse quotient space obtained by the seekers is consistent with the original space after proving the space of the original space satisfying certain conditions. The reversibility of the topology is also determined when the original space to the mapping relationship between the quotient space is determined. When the topology structure is unknown, it can be generated by a topological basis which can be constructed.

Key words: quotient space, saturated set, inverse quotient space, consistency