𝕃-valued variable precision rough sets

Abstract

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 .