Test Cost Constraint Reduction with Common Cost

Test cost is an important issue in cost-sensitive systems. It is what we pay for obtaining a data item of an object. In some applications, there are some common costs and a cost constraint. The common cost is due to the share of the same resources by several tests. The cost constraint is due to limited money, time, or other resources. Recently, the two issues have been addressed independently in cost-sensitive rough sets. In contrast, this paper considers both issues. Our problem is to construct test sets meeting the constraint and preserving the information of decision systems to the highest degree. We propose a heuristic algorithm to deal with this problem. It is based on information gain, test costs, group-memberships, common costs and a non-positive exponent λ. λ is employed in the penalty function such that expensive tests are unlikely to be chosen. Experimental results indicate that the algorithm performs good in terms of the possibility of finding the optimal reduct. Since the optimal setting of λ is often unknown, we can run the algorithm with different λ values and obtain better results.