Vaguely Quantified Rough Sets

The hybridization of rough sets and fuzzy sets has focused on creating an end product that extends both contributing computing paradigms in a conservative way. As a result, the hybrid theory inherits their respective strengths, but also exhibits some weaknesses. In particular, although they allow for gradual membership, fuzzy rough sets are still abrupt in a sense that adding or omitting a single element may drastically alter the outcome of the approximations. In this paper, we revisit the hybridization process by introducing vague quantifiers like “some” or “most” into the definition of upper and lower approximation. The resulting vaguely quantified rough set (VQRS) model is closely related to Ziarko’s variable precision rough set (VPRS) model.