Decision-theoretic rough set model can derive several probabilistic rough set models by providing proper cost functions. Learning cost functions from data automatically is the key to improving the applicability of decision-theoretic rough set model. Many region-related attribute reductions are not appropriate for probabilistic rough set models as the monotonic property of regions does not always hold. In this paper, we propose an optimization representation of decision-theoretic rough set model. An optimization problem is proposed by considering the minimization of the decision cost. Two significant inferences can be drawn from the solution of the optimization problem. Firstly, cost functions and thresholds used in decision-theoretic rough set model can be learned from the given data automatically. An adaptive learning algorithm and a genetic algorithm are designed. Secondly, a minimum cost attribute reduction can be defined. The attribute reduction is interpreted as finding the minimal attribute set to make the decision cost minimum. A heuristic approach and a particle swarm optimization approach are also proposed. The optimization representation can bring some new insights into the research on decision-theoretic rough set model.
['Xiuyi Jia', 'Zhenmin Tang', 'Wenhe Liao', 'Lin Shang']
On an optimization representation of decision-theoretic rough set model