Z. Pawlak introduced Rough Set Theory (RST) which turned out to be one of the most developed mathematical tools for granular computing. In recent years, many researchers dealt with a generalized model of rough sets called variable precision rough sets (VPRS) model, aiming at modeling classification problems involving uncertain or imprecise information. The generalized model not only has all basic mathematical properties of the original model but also has many applications. For example, Beynon and Peel extended previous research by employing the variable precision rough sets (VPRS) model in an experiment to predict between failed and non-failed UK companies. Due to the promising of further applications of VPRST, we study variable precision of generalized rough sets (VPGRS). We generalize VPRST to VPGRS through reflexive relations and provide new lower and upper approximations for VPGRS. We also provide characterizations of lower and upper approximations for VPGRS by introducing minimal neighborhood systems.