Minimum cost attribute reduction in decision-theoretic rough set models

In classical rough set models, attribute reduction generally keeps the positive or non-negative regions unchanged, as these regions do not decrease with the addition of attributes. However, the monotonicity property in decision-theoretic rough set models does not hold. This is partly due to the fact that all regions are determined according to the Bayesian decision procedure. Consequently, it is difficult to evaluate and interpret region-preservation attribute reduction in decision-theoretic rough set models. This paper provides a new definition of attribute reduct for decision-theoretic rough set models. The new attribute reduction is formulated as an optimization problem. The objective is to minimize the cost of decisions. Theoretical analysis shows the meaning of the optimization problem. Both the problem definition and the objective function have good interpretation. A heuristic approach, a genetic approach and a simulated annealing approach to the new problem are proposed. Experimental results on several data sets indicate the efficiency of these approaches.