Test-cost-sensitive attribute reduction of data with normal distribution
  measurement errors
  The measurement error with normal distribution is universal in applications.
Generally, smaller measurement error requires better instrument and higher test
cost. In decision making based on attribute values of objects, we shall 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 four-fold. First, we build a new data
model based on normal distribution measurement errors. With the new data model,
the error range is an ellipse in a two-dimension space. Second, the
covering-based rough set with normal distribution measurement errors is
constructed through the "3-sigma" rule. 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
algorithm is tested on ten UCI (University of California - Irvine) datasets.
The experimental results show that the algorithm is more effective and
efficient than the existing one. This study is a step toward realistic
applications of cost-sensitive learning.
