A fast approach to attribute reduction in incomplete decision systems with tolerance relation-based rough sets
Efficient attribute reduction in large, incomplete decision systems is a challenging problem; existing approaches have time complexities no less than O(?C?2?U?2). This paper derives some important properties of incomplete information systems, then constructs a positive region-based algorithm to solve the attribute reduction problem with a time complexity no more than O(?C?2?U?log?U?). Furthermore, our approach does not change the size of the original incomplete system. Numerical experiments show that the proposed approach is indeed efficient, and therefore of practical value to many real-world problems. The proposed algorithm can be applied to both consistent and inconsistent incomplete decision systems.
attribute reduction incomplete decision system tolerance relation positive region rough set theory