𝕃-valued variable precision rough sets

In this study, we focus on exploring a novel rough sets model, 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: L-fuzzy set H representing the universal set, an L-valued relation on H, and an L-fuzzy subset of H. Also, the classical L-fuzzy rough set, L-valued fuzzy rough set, and L-fuzzy variable precision rough sets can be regarded as special cases of this model. Moreover, through constructive approaches, this paper comprehensively characterizes L-valued variable precision rough sets. Finally, we examine the connection between an L-quasi-topology and L-valued variable precision rough sets on the L-set H.