关键词: 粒计算, 商空间理论, 逆商空间, 饱和性, 可逆性

Abstract: Granular computing is an important research hotspot in artificial intelligence field. As one of the most important granular computing models, the quotient space theory mainly focuses on constructing the quotient space granularity by the false preserving principle, which is granulating from fine to coarse granularity. However, the granulation is an information decreasing and irreversible process. Therefore, this paper focuses on the reversibility of quotient space granularity. Firstly, in order to get the mathematical formal method of reversibly converting granularity from coarse to fine one, it proposes the concept and constructing method of inverse quotient space.Secondly, by analyzing the consistency of quotient space and original space, it demonstrates and analyzes two reversible conditions of the quotient space granularity—defining a bijective function or ensuring the saturability of all open-sets on the original space. This paper aims to further enrich and improve the quotient space granularity transformation theory and granular computing method.

Key words: granular computing, quotient space theory, inverse quotient space, saturability, reversibility