计算机科学与探索2019，Vol.13Issue(5)：884-891,8.DOI:10.3778/j.issn.1673-9418.1804039
商空间粒度的可逆性研究*
Study on Reversibility of Quotient Space Granularity*
摘要
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.关键词
粒计算/商空间理论/逆商空间/饱和性/可逆性Key words
granular computing/ quotient space theory/ inverse quotient space/ saturability/ reversibility分类
信息技术与安全科学引用本文复制引用
陈林书,王加阳,柳媛慧,马庆..商空间粒度的可逆性研究*[J].计算机科学与探索,2019,13(5):884-891,8.基金项目
The National Natural Science Foundation of China under Grant No. 61772031 (国家自然科学基金) （国家自然科学基金）
the Natural Science Foundation of Hunan Province under Grant No. 2018JJ2131 (湖南省自然科学基金) （湖南省自然科学基金）
the Research Project of Steering Committee of Vocational Education for Industrial and Informatization[2018]20 (全国工业和信息化职业教育教学指导委员会科研课题). （全国工业和信息化职业教育教学指导委员会科研课题）
