Multi-objective Optimization Methods Of The Parameters In Decision Theoretic Rough Set Models

As a kind of emerging tools of dealing with uncertain and granular computing, the rough set provides effective and reliable decision-making advices for policy makers by introducing quantitative analysis tool. To deal some issues of the rough set and its related models, such as attribute reduction, threshold learning, Information representation, estimation of conditional probabilities, decision rule acquisition and granularity selection, scholars often apply methods of data mining and pattern recognition. But there are little literatures about the application of optimization method. In this paper, we embark from the optimization method to study the optimization problems of threshold learning in decision theoretic rough set and the selection of neighborhood granule in neighborhood rough sets.For the optimization problem about the threshold in decision-making rough sets, a multi-objective optimization model is put forward to solve the threshold value. This model revises the previous work of the minimization of decision cost model for threshold learning, and then add an objective to present the minimization of boundary region. In the same time, to improve the classification performance of thresholds, two kinds of F-measure constraints are added into our model. In the procedure of model solving, three algorithms are designed under the condition of not considering the F-measure and considering F1-measure and F2-measure. To intuitively response relationship between the two objectives, we choose the multi-objective genetic algorithm by Pareto solution set to show results. In addition, in order to maintain the optimal classification, F-measure is used for the model of a constraint conditions.A comprehensive optimization method has been proposed to solve these problems of the selection of neighborhood radius and the thresholds solving in neighborhood decision theoretic rough set. We get rid of the penalties and then change the single objective function to double objective function based on the existing methods. Considering the optimization problem about the threshold in decision-making rough sets, we construct the optimization model of the neighborhood and thresholds in neighborhood decision theoretic rough set. In order to solve the model, we use the Improving the Strength Pareto Evolutionary Algorithm(SPEA2) to acquire the Pareto solution set. Eight UCI data sets are used to validate the performance of our method.Multi-objective optimization method has been used to study the related parameters in the decision theoretic rough set model in the paper, which then extends the related research ideas of rough sets.