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The Scientific World Journal
Volume 2014, Article ID 382439, 12 pages
http://dx.doi.org/10.1155/2014/382439
Research Article

δ-Cut Decision-Theoretic Rough Set Approach: Model and Attribute Reductions

1School of Computer Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212003, China
2Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information, Nanjing University of Science and Technology, Ministry of Education, Nanjing, Jiangsu 210094, China
3School of Economics and Management, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China
4School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210093, China

Received 5 May 2014; Accepted 6 July 2014; Published 22 July 2014

Academic Editor: Weihua Xu

Copyright © 2014 Hengrong Ju et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Decision-theoretic rough set is a quite useful rough set by introducing the decision cost into probabilistic approximations of the target. However, Yao’s decision-theoretic rough set is based on the classical indiscernibility relation; such a relation may be too strict in many applications. To solve this problem, a δ-cut decision-theoretic rough set is proposed, which is based on the δ-cut quantitative indiscernibility relation. Furthermore, with respect to criterions of decision-monotonicity and cost decreasing, two different algorithms are designed to compute reducts, respectively. The comparisons between these two algorithms show us the following: (1) with respect to the original data set, the reducts based on decision-monotonicity criterion can generate more rules supported by the lower approximation region and less rules supported by the boundary region, and it follows that the uncertainty which comes from boundary region can be decreased; (2) with respect to the reducts based on decision-monotonicity criterion, the reducts based on cost minimum criterion can obtain the lowest decision costs and the largest approximation qualities. This study suggests potential application areas and new research trends concerning rough set theory.