In this study, we focus on exploring a novel rough sets model, $ \mathbb {L} $ L -valued variable precision rough sets, employing a complete residuated lattice within the context of residuated lattices to offer an expansive perspective on lattice truth values. This model comprises three main elements: $ \mathbb {L} $ L -fuzzy set $ \mathbb {H} $ H representing the universal set, an $ \mathbb {L} $ L -valued relation on $ \mathbb {H} $ H , and an $ \mathbb {L} $ L -fuzzy subset of $ \mathbb {H} $ H . Also, the classical $ \mathbb {L} $ L -fuzzy rough set, $ \mathbb {L} $ L -valued fuzzy rough set, and $ \mathbb {L} $ L -fuzzy variable precision rough sets can be regarded as special cases of this model. Moreover, through constructive approaches, this paper comprehensively characterizes $ \mathbb {L} $ L -valued variable precision rough sets. Finally, we examine the connection between an $ \mathbb {L} $ L -quasi-topology and $ \mathbb {L} $ L -valued variable precision rough sets on the $ \mathbb {L} $ L -set $ \mathbb {H} $ H .
$ \mathbb {M}\mathbb {V} $ MV -algebra$ \mathbb {L} $ L -valued relation$ \mathbb {L} $ L -valued rough set$ \mathbb {L} $ L -fuzzy variable precision rough set$ \mathbb {L} $ L -topology
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