On an optimization representation of decision-theoretic rough set model

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.

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• We propose an optimization representation of decision-theoretic rough set model.
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• We can learn thresholds and cost functions from data automatically by solving the optimization problem.
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• We can define a minimum cost attribute reduction based on the optimization representation.
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• An adaptive learning algorithm and a genetic approach to the learning thresholds problem are introduced.
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• A heuristic approach and a particle swarm optimization approach to the new attribute reduction are designed.