In this paper, we discuss the relationship occurring among the basic blocks of rough set theory: approximations, definable sets and exact sets. This is done in a very general framework, named Basic Approximation Space that generalizes and encompasses previous known definitions of Approximation Spaces. In this framework, the lower and upper approximation as well as the boundary and exterior region are independent from each other. Further, definable sets do not coincide with exact sets, the former being defined “a priori” and the latter only “a posteriori” on the basis of the approximations. The consequences of this approach in the particular case of partial partitions are developed and a discussion is started in the case of partial coverings.
Ciucci, D., Mihálydeák, T., Csajbók, Z. (2014). On Definability and Approximations in Partial Approximation Spaces. In Rough Sets and Knowledge Technology (pp.15-26). Springer [10.1007/978-3-319-11740-9_2].
On Definability and Approximations in Partial Approximation Spaces
CIUCCI, DAVIDE ELIO;
2014
Abstract
In this paper, we discuss the relationship occurring among the basic blocks of rough set theory: approximations, definable sets and exact sets. This is done in a very general framework, named Basic Approximation Space that generalizes and encompasses previous known definitions of Approximation Spaces. In this framework, the lower and upper approximation as well as the boundary and exterior region are independent from each other. Further, definable sets do not coincide with exact sets, the former being defined “a priori” and the latter only “a posteriori” on the basis of the approximations. The consequences of this approach in the particular case of partial partitions are developed and a discussion is started in the case of partial coverings.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
