Axiomatization is a lively research direction in fuzzy rough set theory. Fuzzy variable precision rough set (FVPRS) incorporates fault-tolerant factors to fuzzy rough set, so its axiomatic description becomes more complicated and difficult to realize. In this paper, we present an axiomatic approach to FVPRSs based on residuated lattice (L-fuzzy variable precision rough set (LFVPRS)). First, a pair of mappings with three axioms is utilized to characterize the upper (resp., lower) approximation operator of LFVPRS. This is distinct from the characterization on upper (resp., lower) approximation operator of fuzzy rough set, which consists of one mapping with two axioms. Second, utilizing the notion of correlation degree (resp., subset degree) of fuzzy sets, three characteristic axioms are grouped into a single axiom. At last, various special LFVPRS generated by reflexive, symmetric and transitive L-fuzzy relation and their composition are also characterized by axiomatic set and single axiom, respectively.

公理化是模糊粗糙集理论中一个活跃的研究方向。模糊变精度粗糙集(FVPRS)在模糊粗糙集的基础上加入了容错因素，使其公理化描述变得更加复杂且难以实现。在本文中，我们提出了一种基于剩余格（L-模糊变精度粗糙集（LFVPRS））。首先，利用具有三个公理的一对映射来表征 LFVPRS 的上（或下）近似算子。这与模糊粗糙集的上（或下）近似算子的表征不同，后者由具有两个公理的一个映射组成。其次，利用模糊集的相关度（或子集度）的概念，将三个特征公理分组为一个公理。最后，由自反、对称和传递L-模糊关系生成的各种特殊LFVPRS及其组合也分别用公理集和单公理来表征。