Considering L being a complete Heyting algebra, this paper mainly proposes a general framework of L-rough approximate operators in which constructive and axiomatic approaches are used. In the constructive approach, upper and lower L-rough approximate operators are introduced and their connections with L-relations are investigated. In the axiomatic approach, various types of set-theoretic L-operators are defined. It is shown that each type of L-rough approximate operators corresponding to special kind of L-relations, including serial, reflexive, symmetric, transitive, mediate, Euclidean and adjoint L-relations as well as their compositions, can be characterized by single axioms.

中文翻译：

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使用单个公理来表征关于各种L关系的L粗糙近似算子

考虑到L是一个完整的Heyting代数，本文主要提出了一个L粗糙近似算子的通用框架，其中使用了构造和公理方法。在构造方法中，引入了上，下L-粗糙近似算子，并研究了它们与L-关系的联系。在公理方法中，定义了各种类型的集合论L-运算符。结果表明，每种类型的L-近似近似算子都对应于特殊的L-关系，包括序列L，自反L，对称E，传递E，中间Euclidean和伴随L关系及其组成可以通过单个公理来表征。