A heuristic algorithm of attribute reduction in incomplete ordered decision systems.

To analyze the incomplete ordered decision system (IODS), a tolerance dominance relation (TDR) has been introduced in literature, which was an extension of dominance-based rough set approach. Attribute reduction is an important research issue in rough set theory. Because the process of calculating all attribute reductions is a NP-hard problem, this paper mainly focuses on the heuristic algorithm of attribute reduction of IODS by using TDR. Firstly, the properties of rough approximation based on TDR in IODS are reviewed, and a new property of the boundary domain is proposed and proved. Secondly, the concept of approximate quality based on this property is introduced. Then the concept of attribute reduction based on the approximate quality is defined. Thirdly, the significance of attributes based on the approximate quality is defined, and a heuristic algorithm for finding an attribute reduction of IODS is designed by using the significance of attributes as heuristic information. Finally, the experimental results verify the effectiveness of the method proposed in this paper.