中文摘要：

研究了因素空间中概念外延的两种近似方法,即反馈外延外包络和反馈外延内包络。首先从概念及其对立概念出发定义了这两种外延近似,讨论了其与粗糙集的上、下近似的关系,得出它们之间具有一致性的结论,并以此给出了两种包络之间的相关性质。随后,讨论了反馈外延包络对概念外延逼近精度问题,给出了四种改善方法。

英文摘要：

This paper aims to study the two approximate methods about the extension of concept, i. e. , outer-enveloping and inner-enveloping of feedback extension. First, we construct the two approximations at the sight of the concept itself and its inverse concept. Then we discuss the relationship between the approximations and upper and lower approximations in the rough set theory. It reveals that they have consistency. Some related properties existing between the two envelopes are showed. Subsequently, we also discuss the precision problems of the envelopes in approximating the extension of concept and then four improve methods are proposed.