%0 Journal Article
%T 双论域下多粒度模糊粗糙集上下近似的包含关系
%A 胡志勇
%A 米据生
%A 冯涛
%A 姚爱梦
%J 智能系统学报
%D 2019
%R 10.11992/tis.201804046
%X 针对双论域上集合的多粒度乐观与悲观上下近似不具有包含关系的问题，本文给出了双论域上集合的多粒度上下近似具有包含关系的一个充分条件，进而采用标准化的方法将不具有包含关系的上下近似转化为具有包含关系的上下近似。通过实例验证，该方法能有效解决双论域下多粒度模糊粗糙集上下近似具有包含关系的问题。</br>To solve the problem that the upper and lower approximations of multigranularity rough set in two universe may no longer have an inclusion relation, this paper will present a sufficient condition for the inclusion relation of the upper and lower approximations in two universes. Furthermore, we use the standardized method to transform upper and lower approximations with no inclusion relation into upper and lower approximations with an inclusion relation. It is verified by an example that this method can effectively solve the problem that the upper and lower approximations of the multigranularity fuzzy rough set in two universes have inclusion relation
%K 模糊集
%K 粗糙集
%K 双论域
%K 多粒度
%K 上近似
%K 下近似
%K 标准化
%K 包含关系
%K 充分条件&lt
%K /br&gt
%K fuzzy set
%K rough set
%K dual domain
%K multi-granularity
%K upper approximation
%K lower approximation
%K standardized method
%K inclusion relation
%K sufficient condition
%U http://tis.hrbeu.edu.cn/oa/darticle.aspx?type=view&id=201804046