Rough set theory provides a very useful research method for knowledge structures. This paper outlines a possible relationship between knowledge structures and rough sets. We characterize knowledge spaces with rough upper approximations. In particular, we discuss the knowledge structures induced by a skill map via disjunctive and conjunctive models by means of rough set approaches and identify the conditions under which the knowledge structures induced by a skill multimap are closed under union or intersection. The covering reduction technique is used to identify the minimal skill maps. Finally, we define the knowledge structures induced via the disjunctive model by skill multimaps and study an open problem (Falmagne and Doignon (2011) [3, Chap. 6, Question 7]: Under which condition on a skill multimap is the delineated structure closed under intersection?

粗糙集理论为知识结构提供了一种非常有用的研究方法。本文概述了知识结构和粗糙集之间可能的关系。我们用粗略的上近似来表征知识空间。特别是，我们通过粗糙集方法通过分离和连接模型讨论了技能图诱导的知识结构，并确定了技能多图诱导的知识结构在联合或交集下封闭的条件。覆盖减少技术用于识别最小技能图。最后，我们定义了由技能多重映射通过析取模型诱导的知识结构，并研究了一个开放问题（Falmagne 和 Doignon（2011）[3，第 6 章，问题 7]：