Vagueness and Uncertainty: An F-Rough Set Perspective

F-rough sets are the first dynamical rough set model for a family of information systems (decision systems). This chapter investigates vagueness and uncertainty from the viewpoints of F-rough sets. Some indexes, including two types of F-roughness, two types of F-membership-degree and F-dependence degree etc., are defined. Each of these indexes may be a set of number, not like other vague and uncertain indexes in Pawlak rough sets. These indexes extend those of Pawlak rough sets, and indicate vagueness and uncertainty in a family of information subsystems (decision subsystems). Moreover, these indexes themselves also include vagueness and uncertainty, namely, vagueness of vagueness and uncertainty of uncertainty. Further, we investigate some interesting properties of these indexes.