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

Implicator-conjunctor based models of fuzzy rough sets: definitions and properties

Ever since the first hybrid fuzzy rough set model was proposed in the early 1990' s, many researchers have focused on the definition of the lower and upper approximation of a fuzzy set by means of a fuzzy relation. In this paper, we review those proposals which generalize the logical connectives and quantifiers present in the rough set approximations by means of corresponding fuzzy logic operations. We introduce a general model which encapsulates all of these proposals, evaluate it w.r.t. a number of desirable properties, and refine the existing axiomatic approach to characterize lower and upper approximation operators