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

摘要： 粒计算是当前计算智能研究领域中模拟人类思维和解决复杂问题的新方法。商空间理论是粒度计算的三种主要方法之一。在商空间理论的基础上，分析逆商空间的相关性质，并对商空间的逆商空间与其原空间的一致性进行分析，证明了满足一定条件的原空间导出商空间后，求逆商得到的逆商空间与原空间具有一致性。原空间到其商空间的映射关系确定后，其拓扑的可逆性也随之确定，在未知拓扑结构时可以构造拓扑基生成具有可逆性质的拓扑。

关键词: 商空间, 饱和集, 逆商空间, 一致性