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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 946070, 12 pages
Research Article

Test-Cost-Sensitive Attribute Reduction of Data with Normal Distribution Measurement Errors

Laboratory of Granular Computing, Zhangzhou Normal University, Zhangzhou 363000, China

Received 31 December 2012; Accepted 1 March 2013

Academic Editor: Hung Nguyen-Xuan

Copyright © 2013 Hong Zhao 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.


The measurement error with normal distribution is universal in applications. Generally, smaller measurement error requires better instrument and higher test cost. In decision making, we will select an attribute subset with appropriate measurement error to minimize the total test cost. Recently, error-range-based covering rough set with uniform distribution error was proposed to investigate this issue. However, the measurement errors satisfy normal distribution instead of uniform distribution which is rather simple for most applications. In this paper, we introduce normal distribution measurement errors to covering-based rough set model and deal with test-cost-sensitive attribute reduction problem in this new model. The major contributions of this paper are fourfold. First, we build a new data model based on normal distribution measurement errors. Second, the covering-based rough set model with measurement errors is constructed through the “3-sigma” rule of normal distribution. With this model, coverings are constructed from data rather than assigned by users. Third, the test-cost-sensitive attribute reduction problem is redefined on this covering-based rough set. Fourth, a heuristic algorithm is proposed to deal with this problem. The experimental results show that the algorithm is more effective and efficient than the existing one. This study suggests new research trends concerning cost-sensitive learning.