Multi-objective optimization method for thresholds learning and neighborhood computing in a neighborhood based decision-theoretic rough set model

Recently, a neighborhood based decision-theoretic rough set (NDTRS) model was proposed to deal with the general data which contained numerical values and noisy values simultaneously. However, it still suffered from the issue of granularity selection and the relationship between the thresholds and the neighborhood was also not investigated in depth. In this paper, a multi-objective optimization model for NDTRS to learn the thresholds and select the granularity (compute the neighborhood) comprehensively is proposed. In this model, three significant problems: decreasing the size of the boundary region, decreasing the overall decision cost for the three types of rules, and increasing the size of the neighborhood are taken into consideration. We use 10 UCI datasets to validate the performance of our method. With the Improved Strength Pareto Evolutionary Algorithm (SPEA2), the Pareto optimal solutions are obtained automatically. The experimental results demonstrate the trade-off among the three objectives and show that the thresholds and neighborhoods obtained by our method are more intuitive.