Journal paper accepted
26/02/20/08:36 Filed in: Journal paper
E. Ramírez-Poussa, N. Madrid, J. Medina. Rough Sets based on Galois connections. Applied Mathematics and Computer Science 30(2):299-313, 2020.
ABSTRACT Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of the approximation operators are based on an indiscernibility relation, which is an equivalence relation. Later, different papers have motivated the possibility of considering arbitrary relations nevertheless, when arbitrary relations are considered, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution of the arisen problems by presenting an alternative definition of the approximation operators based on the closure and the interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks.
ABSTRACT Rough set theory is an important tool to extract knowledge from relational databases. The original definitions of the approximation operators are based on an indiscernibility relation, which is an equivalence relation. Later, different papers have motivated the possibility of considering arbitrary relations nevertheless, when arbitrary relations are considered, the original definitions given by Pawlak may lose fundamental properties. This paper proposes a possible solution of the arisen problems by presenting an alternative definition of the approximation operators based on the closure and the interior operators obtained from an isotone Galois connection. We prove that the proposed definition satisfies interesting properties and that it also improves object classification tasks.